Academic literature on the topic 'Kuznetsov equation'

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Journal articles on the topic "Kuznetsov equation"

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Li, Changzhao, and Juan Zhang. "Lie Symmetry Analysis and Exact Solutions of Generalized Fractional Zakharov-Kuznetsov Equations." Symmetry 11, no. 5 (2019): 601. http://dx.doi.org/10.3390/sym11050601.

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This paper considers the Lie symmetry analysis of a class of fractional Zakharov-Kuznetsov equations. We systematically show the procedure to obtain the Lie point symmetries for the equation. Accordingly, we study the vector fields of this equation. Meantime, the symmetry reductions of this equation are performed. Finally, by employing the obtained symmetry properties, we can get some new exact solutions to this fractional Zakharov-Kuznetsov equation.
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Kaltenbacher, Barbara, and Vanja Nikolić. "The Jordan–Moore–Gibson–Thompson Equation: Well-posedness with quadratic gradient nonlinearity and singular limit for vanishing relaxation time." Mathematical Models and Methods in Applied Sciences 29, no. 13 (2019): 2523–56. http://dx.doi.org/10.1142/s0218202519500532.

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In this paper, we consider the Jordan–Moore–Gibson–Thompson equation, a third-order in time wave equation describing the nonlinear propagation of sound that avoids the infinite signal speed paradox of classical second-order in time strongly damped models of nonlinear acoustics, such as the Westervelt and the Kuznetsov equation. We show well-posedness in an acoustic velocity potential formulation with and without gradient nonlinearity, corresponding to the Kuznetsov and the Westervelt nonlinearities, respectively. Moreover, we consider the limit as the parameter of the third-order time derivati
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Khalique, Chaudry Masood. "Exact Explicit Solutions and Conservation Laws for a Coupled Zakharov-Kuznetsov System." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/461327.

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We study a coupled Zakharov-Kuznetsov system, which is an extension of a coupled Korteweg-de Vries system in the sense of the Zakharov-Kuznetsov equation. Firstly, we obtain some exact solutions of the coupled Zakharov-Kuznetsov system using the simplest equation method. Secondly, the conservation laws for the coupled Zakharov-Kuznetsov system will be constructed by using the multiplier approach.
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Rozanova, Anna. "The Khokhlov–Zabolotskaya–Kuznetsov equation." Comptes Rendus Mathematique 344, no. 5 (2007): 337–42. http://dx.doi.org/10.1016/j.crma.2007.01.010.

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Tao, Zhao-Ling. "Variational Principles for Some Nonlinear Wave Equations." Zeitschrift für Naturforschung A 63, no. 5-6 (2008): 237–40. http://dx.doi.org/10.1515/zna-2008-5-601.

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Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear wave equations arising in physics, including the Pochhammer-Chree equation, Zakharov-Kuznetsov equation, Korteweg-de Vries equation, Zhiber-Shabat equation, Kawahara equation, and Boussinesq equation.
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Zayed, E. M. E., and K. A. E. Alurrfi. "The Generalized Projective Riccati Equations Method for Solving Nonlinear Evolution Equations in Mathematical Physics." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/259190.

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We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
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Vinita and S. Saha Ray. "Symmetry analysis with similarity reduction, new exact solitary wave solutions and conservation laws of (3 + 1)-dimensional extended quantum Zakharov–Kuznetsov equation in quantum physics." Modern Physics Letters B 35, no. 09 (2021): 2150163. http://dx.doi.org/10.1142/s0217984921501633.

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A recently defined (3+1)-dimensional extended quantum Zakharov–Kuznetsov (QZK) equation is examined here by using the Lie symmetry approach. The Lie symmetry analysis has been used to obtain the varieties in invariant solutions of the extended Zakharov–Kuznetsov equation. Due to existence of arbitrary functions and constants, these solutions provide a rich physical structure. In this paper, the Lie point symmetries, geometric vector field, commutative table, symmetry groups of Lie algebra have been derived by using the Lie symmetry approach. The simplest equation method has been presented for
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Dekkers, Adrien, and Anna Rozanova-Pierrat. "Cauchy problem for the Kuznetsov equation." Discrete & Continuous Dynamical Systems - A 39, no. 1 (2019): 277–307. http://dx.doi.org/10.3934/dcds.2019012.

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Linares, Felipe, Mahendra Panthee, Tristan Robert, and Nikolay Tzvetkov. "On the periodic Zakharov-Kuznetsov equation." Discrete & Continuous Dynamical Systems - A 39, no. 6 (2019): 3521–33. http://dx.doi.org/10.3934/dcds.2019145.

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Cossetti, Lucrezia, Luca Fanelli, and Felipe Linares. "Uniqueness results for Zakharov-Kuznetsov equation." Communications in Partial Differential Equations 44, no. 6 (2019): 504–44. http://dx.doi.org/10.1080/03605302.2019.1581803.

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Dissertations / Theses on the topic "Kuznetsov equation"

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Rozanova-Pierrat, Anna. "Equation de Khokhlov-Zabolotskaya-Kuznetsov. Analyse Mathématique, Validation de l'approximation et Méthode de Contrôle." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2006. http://tel.archives-ouvertes.fr/tel-00126487.

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Ce travail se compose de deux parties. Dans la première, nous considérons l'équation de Khokhlov-Zabolotskaya-Kuznetsov (KZK) $(u_t - u u_x -\beta u_{xx})_x -\gamma \Delta_y u =0$ dans les espaces de Sobolev des fonctions p\ériodiques sur $x$ de valeur moyenne nulle. La déivation de l'\équation KZK à partir des équations de Navier-Stokes isentropiques non linéaires et de l'approximation de leurs solutions (pour les cas visqueux et non visqueux), les résultats de l'existence, de l'unicité, de la stabilité et du blow-up de la solution de KZK sont obtenus ainsi qu'un résultat sur l'existence d'un
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Munro, Susan. "The derivation of a modified Zakharov Kuznetsov equation and the stability of its solutions." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248712.

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Rozanova, Anna. "Equation de Khokhlov-Zabolotskaya-Kuznetsov : analyse mathématique, validation de l'approximation et méthode de contrôle." Paris 6, 2006. https://tel.archives-ouvertes.fr/tel-00126487.

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On considère l’équation de Khokhlov-Zabolotskaya-Kuznetsov (KZK) dans les espaces de Sobolev des fonctions périodiques sur x de valeur moyenne nulle. La dérivation de l’équation KZK à partir des équations de Navier-Stokes isentropiques et de l’approximation de leurs solutions (pour les cas visqueux et non visqueux), les résultats de l’existence, de l’unicité, de la stabilité, du blow-up, de contrôlabilité sont obtenus ainsi qu’un résultat sur l’existence d’une solution régulière du système de Navier-Stokes dans le demi-espace avec conditions aux limites périodiques en temps et de valeur moyenn
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Dekkers, Adrien. "Analyse mathématique de l'équation de Kuznetsov : problème de Cauchy, questions d'approximations et problèmes aux bords fractals." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLC019/document.

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Dans le contexte de l’acoustique on a systématisé la dérivation de modèles nonlinéaires(l’équation de Kuznetsov, l’équation KZK et la NPE). On a estimé le temps pourlequel des solutions régulières de ces modèles restent proches des solutions des systèmes deNavier-Stokes/Euler compressibles isentropiques (en précisant leur plus faible régularité) etétabli les résultats analogues entre les solutions des équations de KZK, NPE et Westerveltpar rapport à la solution de l’équation de Kuznetsov. Pour ce faire, on a étudié l’équationde Kuznetsov en commençant par le problème de Cauchy dans les cas vis
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Sun, Weizhou. "LOCAL DISCONTINUOUS GALERKIN METHOD FOR KHOKHLOV-ZABOLOTSKAYA-KUZNETZOV EQUATION AND IMPROVED BOUSSINESQ EQUATION." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1480327264817905.

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Cunha, Alysson Tobias Ribeiro 1976. "O problema de Cauchy para a equação de Benjamin-Ono-Zakharov-Kuznetsov." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306888.

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Orientador: Ademir Pastor Ferreira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-24T23:55:39Z (GMT). No. of bitstreams: 1 Cunha_AlyssonTobiasRibeiro_D.pdf: 2613588 bytes, checksum: a1484c40a841c1479e707e39620338b7 (MD5) Previous issue date: 2014<br>Resumo: O resumo poderá ser visualizado no texto completo da tese digital<br>Abstract: The abstract is available with the full electronic digital document<br>Doutorado<br>Matematica<br>Doutor em Matemática
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Berglund, Mårten. "Green growth? A consumption perspective on Swedish environmental impact trends using input–output analysis." Thesis, Uppsala universitet, Globala energisystem, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-157800.

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Consumption-based environmental impact trends for the Swedish economy have been generated and analysed in order to determine their levels compared to official production-based data, and to determine whether or not the Swedish economy has decoupled growth in domestic final demand from worldwide environmental impact. Three energy resources (oil, coal and gas use, as well as their aggregate fossil fuel use) and seven emissions (CO2, CH4, N2O, SO2, NOx, CO and NMVOC, as well as the aggregate CO2 equivalents) were studied. An augmented single-regional input–output model has been deployed, with worl
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Adem, Khadijo Rashid. "Exact solutions and conversation laws of (2+1) - dimensional zarkharov-kuznetsov modified equal width equation / Khadijo Rashid Adem." Thesis, 2011. http://hdl.handle.net/10394/15795.

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In this dissertation exact solutions of the (2+1) dimensional Zakharov-Kuznetsov modified equal width equation arc obtained. The Lie group analysis is used to carry out the integration of this equation. The solutions obtained include the non-topological soliton solution, cnoidal waves and the traveling wave solutions. Also exact solutions to the Zakharov-Kuznetsov modified equal width equation with power Jaw nonlinearity arc obtained. The Lie symmetry approach along with the simplest equation method is used to obtain these solutions. Moreover, conservation laws of the generalized Zarkharov-Kuz
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Moleleki, Letlhogonolo Daddy. "Symmetry reductions, exact solutions and conservation laws of a variable coefficient (2+1)-dimensional zakharov-kuznetsov equation / Letlhogonolo Daddy Moleleki." Thesis, 2011. http://hdl.handle.net/10394/14404.

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This research studies two nonlinear problems arising in mathematical physics. Firstly the Korteweg-de Vrics-Burgers equation is considered. Lie symmetry method is used to obtain t he exact solutions of Korteweg-de Vries-Burgers equation. Also conservation laws are obtained for this equation using the new conservation theorem. Secondly, we consider the generalized (2+ 1)-dimensional Zakharov-Kuznctsov (ZK) equation of time dependent variable coefficients from the Lie group-theoretic point of view. We classify the Lie point symmetry generators to obtain the optimal system of one-dimensional suba
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Niu, Yaying. "Three-Dimensional Nonlinear Acoustical Holography." Thesis, 2013. http://hdl.handle.net/1969.1/149484.

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Nearfield Acoustical Holography (NAH) is an acoustic field visualization technique that can be used to reconstruct three-dimensional (3-D) acoustic fields by projecting two-dimensional (2-D) data measured on a hologram surface. However, linear NAH algorithms developed and improved by many researchers can result in significant reconstruction errors when they are applied to reconstruct 3-D acoustic fields that are radiated from a high-level noise source and include significant nonlinear components. Here, planar, nonlinear acoustical holography procedures are developed that can be used to recon
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Book chapters on the topic "Kuznetsov equation"

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Faminskii, Andrei V. "On One Control Problem for Zakharov–Kuznetsov Equation." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04459-6_29.

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Biagioni, H. A., and F. Linares. "Well-posedness Results for the Modified Zakharov-Kuznetsov Equation." In Nonlinear Equations: Methods, Models and Applications. Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8087-9_13.

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Farah, Luiz Gustavo, Justin Holmer, and Svetlana Roudenko. "Instability of Solitons in the 2d Cubic Zakharov-Kuznetsov Equation." In Nonlinear Dispersive Partial Differential Equations and Inverse Scattering. Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4939-9806-7_6.

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Faminskii, A. V., and A. P. Antonova. "On Internal Regularity of Solutions to the Initial Value Problem for the Zakharov–Kuznetsov Equation." In Progress in Partial Differential Equations. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00125-8_3.

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Lannes, David, Felipe Linares, and Jean-Claude Saut. "The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation." In Studies in Phase Space Analysis with Applications to PDEs. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6348-1_10.

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Das, Amiya. "Exact Traveling Wave Solutions and Bifurcation Analysis for Time Fractional Dual Power Zakharov-Kuznetsov-Burgers Equation." In Mathematical Modelling and Scientific Computing with Applications. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1338-1_3.

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Dynkin, E. B. "Markov Processes and Their Applications to Partial Differential Equations: Kuznetsov’s Contributions." In Advances in Superprocesses and Nonlinear PDEs. Springer US, 2013. http://dx.doi.org/10.1007/978-1-4614-6240-8_1.

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"Well-posedness of the Westervelt and the Kuznetsov equation with nonhomogeneous Neumann boundary conditions." In Conference Publications 2011. AIMS Press, 2011. http://dx.doi.org/10.3934/proc.2011.2011.763.

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Mandi, Laxmikanta, Kaushik Roy, and Prasanta Chatterjee. "Approximate Analytical Solution of Nonlinear Evolution Equations." In Selected Topics in Plasma Physics. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.93176.

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Analytical solitary wave solution of the dust ion acoustic waves (DIAWs) is studied in the frame-work of Korteweg-de Vries (KdV), damped force Korteweg-de Vries (DFKdV), damped force modified Korteweg-de Vries (DFMKdV) and damped forced Zakharov-Kuznetsov (DFZK) equations in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, Maxwellian distributed electrons and neutral particles. Using reductive perturbation technique (RPT), the evolution equations are obtained for DIAWs.
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Prakash, Amit, and Hardish Kaur. "A New Numerical Method for a Fractional Model of Non-Linear Zakharov–Kuznetsov Equations via Sumudu Transform." In Methods of Mathematical Modelling. CRC Press, 2019. http://dx.doi.org/10.1201/9780429274114-11.

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Conference papers on the topic "Kuznetsov equation"

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Söderholm, Lars H. "On the Kuznetsov equation and higher order nonlinear acoustics equations." In 15th international symposium on nonlinear acoustics: Nonlinear acoustics at the turn of the millennium. AIP, 2000. http://dx.doi.org/10.1063/1.1309189.

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Khalique, Chaudry Masood, and Karabo Plaatjie. "A study of two-dimensional Zakharov-Kuznetsov-Burgers equation." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114172.

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Xiaofeng Zhao and Robert J. McGough. "The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation with power law attenuation." In 2014 IEEE International Ultrasonics Symposium (IUS). IEEE, 2014. http://dx.doi.org/10.1109/ultsym.2014.0554.

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Guner, Ozkan, Esin Aksoy, Ahmet Bekir, and Adem C. Cevikel. "Various methods for solving time fractional KdV-Zakharov-Kuznetsov equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952085.

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Magalakwe, Gabriel, and Chaudry Masood Khalique. "Conservation laws for a (3 + 1)-dimensional extended Zakharov-Kuznetsov equation." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114177.

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Baskonus, Haci Mehmet, Gülnur Yel, and Hasan Bulut. "Novel wave surfaces to the fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992767.

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Mohamed, Mohamed S., Faisal Al-Malki, and Khaled A. Gepreel. "Approximate solution for fractional Zakharov-Kuznetsov equation using the fractional complex transform." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825925.

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Baskonus, Haci Mehmet, Dilara Altan Koç, Mustafa Gülsu, and Hasan Bulut. "New wave simulations to the (3+1)-dimensional modified Kdv-Zakharov-Kuznetsov equation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992768.

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Korkmaz, Alper, and Ozlem Ersoy Hepson. "Hyperbolic tangent solution to the conformable time fractional Zakharov-Kuznetsov equation in 3D space." In 6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5020472.

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Kanagawa, Tetsuya, Takeru Yano, Junya Kawahara, Kazumichi Kobayashi, Masao Watanabe, and Shigeo Fujikawa. "Nonlinear Propagation of Sound Beam in Nonuniform Bubbly Liquids." In ASME-JSME-KSME 2011 Joint Fluids Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/ajk2011-33017.

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Nonlinear propagation of weakly diffracted sound beams in a weakly nonuniform bubbly liquid is analytically studied based on the method of multiple scales and scaling relations of some physical parameters. The system of basic equations consists of the conservation equations of mass and momentum for gas and liquid in a two-flui model, the Keller equation for bubble wall, the state equations for gas and liquid, and so on. The compressibility of liquid is taken into account and this leads to the wave attenuation due to bubble oscillations. It is assumed that the spatial distribution of the number
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Reports on the topic "Kuznetsov equation"

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Muhlestein, Michael, and Carl Hart. Numerical analysis of weak acoustic shocks in aperiodic array of rigid scatterers. Engineer Research and Development Center (U.S.), 2020. http://dx.doi.org/10.21079/11681/38579.

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Nonlinear propagation of shock waves through periodic structures have the potential to exhibit interesting phenomena. Frequency content of the shock that lies within a bandgap of the periodic structure is strongly attenuated, but nonlinear frequency-frequency interactions pumps energy back into those bands. To investigate the relative importance of these propagation phenomena, numerical experiments using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation are carried out. Two-dimensional propagation through a periodic array of rectangular waveguides is per-formed by iteratively using the output
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