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Journal articles on the topic 'Parametric solutions'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Dempe, S., and D. Pallaschke. "Quasidifferntiability of optimal solutions in parametric optimal solutions in parametric nonlinear optimization." Optimization 40, no. 1 (1997): 1–24. http://dx.doi.org/10.1080/02331939708844295.

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2

Pérez-Dı́az, Sonia, and J. Rafael Sendra. "Computing all parametric solutions for blending parametric surfaces." Journal of Symbolic Computation 36, no. 6 (2003): 925–64. http://dx.doi.org/10.1016/s0747-7171(03)00072-5.

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3

Cavaliere, F., S. Zlotnik, R. Sevilla, X. Larrayoz, and P. Díez. "Nonintrusive parametric solutions in structural dynamics." Computer Methods in Applied Mechanics and Engineering 389 (February 2022): 114336. http://dx.doi.org/10.1016/j.cma.2021.114336.

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4

Werner, M. J., and P. D. Drummond. "Simulton solutions for the parametric amplifier." Journal of the Optical Society of America B 10, no. 12 (1993): 2390. http://dx.doi.org/10.1364/josab.10.002390.

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5

Song, J. M., and W. C. Chew. "Moment method solutions using parametric geometry." Journal of Electromagnetic Waves and Applications 9, no. 1-2 (1995): 71–83. http://dx.doi.org/10.1163/156939395x00253.

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6

Díez, Pedro, Sergio Zlotnik, and Antonio Huerta. "Generalized parametric solutions in Stokes flow." Computer Methods in Applied Mechanics and Engineering 326 (November 2017): 223–40. http://dx.doi.org/10.1016/j.cma.2017.07.016.

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7

Lester, D. R., M. Rudman, G. Metcalfe, and H. M. Blackburn. "Global parametric solutions of scalar transport." Journal of Computational Physics 227, no. 6 (2008): 3032–57. http://dx.doi.org/10.1016/j.jcp.2007.10.015.

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8

McClendon, J. F. "Continuous approximate solutions in parametric optimization." Acta Applicandae Mathematicae 15, no. 3 (1989): 275–300. http://dx.doi.org/10.1007/bf00047533.

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9

Marinković, Silvana, and Dragić Banković. "Subsumptive general solutions and parametric general solutions of Post equations." Information Sciences 187 (March 2012): 121–28. http://dx.doi.org/10.1016/j.ins.2011.09.041.

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10

Qiao, Zhijun, and Shengtai Li. "A New Integrable Hierarchy, Parametric Solutions and Traveling Wave Solutions." Mathematical Physics, Analysis and Geometry 7, no. 4 (2004): 289–308. http://dx.doi.org/10.1007/s11040-004-3090-8.

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11

Skalna, Iwona, and Milan Hladík. "Direct and iterative methods for interval parametric algebraic systems producing parametric solutions." Numerical Linear Algebra with Applications 26, no. 3 (2019): e2229. http://dx.doi.org/10.1002/nla.2229.

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12

Papageorgiou, Nikolaos S., and George Smyrlis. "Positive solutions for parametric $p$-Laplacian equations." Communications on Pure and Applied Analysis 15, no. 5 (2016): 1545–70. http://dx.doi.org/10.3934/cpaa.2016002.

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13

Kim, K. H., and F. W. Roush. "Undecidability of parametric solutions of polynomial equations." Proceedings of the American Mathematical Society 118, no. 2 (1993): 345. http://dx.doi.org/10.1090/s0002-9939-1993-1132414-5.

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14

Volosova, Alexandra K., and Konstantin Alexandrovich Volosov. "Construction Solutions of PDE in Parametric Form." International Journal of Mathematics and Mathematical Sciences 2009 (2009): 1–17. http://dx.doi.org/10.1155/2009/319269.

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The new important property of wide class PDE was found solely by K. A. Volosov. We make an arbitrary replacement of variables. In the case of two independent variables , then it always gives the possibility of expressing all PDE second and more order as . This is a linear algebraic equations system with regards derivatives to old variables , on new variables . This system has the unique solution. In the case of three and more independent variables then it gives the possibility of expressing PDE second order as , if we do same compliment proposes. In the present paper, we suggest a new method f

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15

Pötzsche, Christian. "Robustness of hyperbolic solutions under parametric perturbations." Journal of Difference Equations and Applications 15, no. 8-9 (2009): 803–19. http://dx.doi.org/10.1080/10236190802357644.

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16

Smyrlis, George, and Nikolaos S. Papageorgiou. "Positive solutions for nonlinear nonhomogeneous parametric equations." Topological Methods in Nonlinear Analysis 46, no. 1 (2015): 1. http://dx.doi.org/10.12775/tmna.2015.033.

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17

Wu, Ai-Guo, Lingling Lv, Guang-Ren Duan, and Wanquan Liu. "Parametric solutions to Sylvester-conjugate matrix equations." Computers & Mathematics with Applications 62, no. 9 (2011): 3317–25. http://dx.doi.org/10.1016/j.camwa.2011.08.034.

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18

Papageorgiou, Nikolaos S., Calogero Vetro, and Francesca Vetro. "Solutions for parametric double phase Robin problems." Asymptotic Analysis 121, no. 2 (2021): 159–70. http://dx.doi.org/10.3233/asy-201598.

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We consider a parametric double phase problem with Robin boundary condition. We prove two existence theorems. In the first the reaction is ( p − 1 )-superlinear and the solutions produced are asymptotically big as λ → 0 + . In the second the conditions on the reaction are essentially local at zero and the solutions produced are asymptotically small as λ → 0 + .

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19

Randolph, Mark F., Donghee Seo, and David J. White. "Parametric Solutions for Slide Impact on Pipelines." Journal of Geotechnical and Geoenvironmental Engineering 136, no. 7 (2010): 940–49. http://dx.doi.org/10.1061/(asce)gt.1943-5606.0000314.

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20

Mustafa, M. T. "New parametric solutions of some Abel equations." Miskolc Mathematical Notes 17, no. 2 (2017): 957. http://dx.doi.org/10.18514/mmn.2017.1246.

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21

Bekov, A. A., and S. B. Momynov. "Parametric solutions of the Gylden–Meshchersky problem." International Journal of Non-Linear Mechanics 116 (November 2019): 195–99. http://dx.doi.org/10.1016/j.ijnonlinmec.2019.06.009.

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22

Wen, Zhenshu. "Extension on Bifurcations of Traveling Wave Solutions for a Two-Component Fornberg-Whitham Equation." Abstract and Applied Analysis 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/704931.

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Fan et al. studied the bifurcations of traveling wave solutions for a two-component Fornberg-Whitham equation. They gave a part of possible phase portraits and obtained some uncertain parametric conditions for solitons and kink (antikink) solutions. However, the exact explicit parametric conditions have not been given for the existence of solitons and kink (antikink) solutions. In this paper, we study the bifurcations for the two-component Fornberg-Whitham equation in detalis, present all possible phase portraits, and give the exact explicit parametric conditions for various solutions. In addi

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23

Mosaddeghi, Masoud. "Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation." Journal of Applied Mathematics 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/170946.

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By using bifurcation theory of planar ordinary differential equations all different bounded travelling wave solutions of the generalized Zakharov equation are classified in to different parametric regions. In each of these parametric regions the exact explicit parametric representation of all solitary, kink (antikink), and periodic wave solutions as well as their numerical simulation and their corresponding phase portraits are obtained.

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24

Li, Jibin. "On the Exact Traveling Wave Solutions of (2 + 1)-Dimensional Higher Order Broer–Kaup Equation." International Journal of Bifurcation and Chaos 24, no. 01 (2014): 1450007. http://dx.doi.org/10.1142/s0218127414500072.

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In this paper, we study the dynamical behavior and exact parametric representations of all traveling wave solutions for (2 + 1)-dimensional higher order Broer–Kaup equation. By using the method of dynamical systems, under different parametric conditions, for the solution component U, exact monotonic and nonmonotonic kink wave solutions, two-peak wave solutions, periodic wave solutions, as well as unbounded traveling wave solutions are obtained. Exact wave profiles of traveling wave solutions for all solution components U, V, W, P are shown.

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25

Choudhry, Ajai. "A new approach to the Tarry–Escott problem." International Journal of Number Theory 13, no. 02 (2017): 393–417. http://dx.doi.org/10.1142/s1793042117500233.

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In this paper we describe a new method of obtaining ideal solutions of the well-known Tarry–Escott problem, that is, the problem of finding two distinct sets of integers [Formula: see text] and [Formula: see text] such that [Formula: see text], [Formula: see text], where [Formula: see text] is a given positive integer. When [Formula: see text], only a limited number of parametric/numerical ideal solutions of the Tarry–Escott problem are known. In this paper, by applying the new method mentioned above, we find several new parametric ideal solutions of the problem when [Formula: see text]. The i

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26

Tang, Shengqiang, and Shu Xia. "Bifurcations of Traveling Wave Solutions for the Coupled Higgs Field Equation." International Journal of Differential Equations 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/547617.

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By using the bifurcation theory of dynamical systems, we study the coupled Higgs field equation and the existence of new solitary wave solutions, and uncountably infinite many periodic wave solutions are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. All exact explicit parametric representations of the above waves are determined.

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27

Karunakar, Perumandla, and Snehashish Chakraverty. "Solution of interval shallow water wave equations using homotopy perturbation method." Engineering Computations 35, no. 4 (2018): 1610–24. http://dx.doi.org/10.1108/ec-12-2016-0449.

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Purpose This paper aims to present solutions of uncertain linear and non-linear shallow water wave equations. The uncertainty has been taken as interval and one-dimensional interval shallow water wave equations have been solved by homotopy perturbation method (HPM). In this study, basin depth and initial conditions have been taken as interval and the single parametric concept has been used to handle the interval uncertainty. Design/methodology/approach HPM has been used to solve interval shallow water wave equation with the help of single parametric concept. Findings Previously, few authors fo

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28

Protsenko, E., V. Mironenko, and D. Sopov. "CHOICE OF OPTIMAL ARCHITECTURALCONSTRUCTIVE SOLUTIONS DURING PARAMETRIC MODELING." Scientific Bulletin of Civil Engineering 97, no. 3 (2019): 30–36. http://dx.doi.org/10.29295/2311-7257-2019-97-3-30-36.

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29

Aizicovici, Sergiu, Nikolaos S. Papageorgiou, and Vasile Staicu. "Positive Solutions for Parametric Nonlinear Nonhomogeneous Robin Problems." Funkcialaj Ekvacioj 61, no. 3 (2018): 285–313. http://dx.doi.org/10.1619/fesi.61.285.

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30

Matsuno, Yoshimasa. "Parametric solutions of the generalized short pulse equations." Journal of Physics A: Mathematical and Theoretical 53, no. 10 (2020): 105202. http://dx.doi.org/10.1088/1751-8121/ab6f18.

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31

Papageorgiou, Nikolaos S., Vicenţiu D. Rădulescu, and Dušan D. Repovš. "Positive solutions for nonlinear nonhomogeneous parametric Robin problems." Forum Mathematicum 30, no. 3 (2018): 553–80. http://dx.doi.org/10.1515/forum-2017-0124.

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AbstractWe study a parametric Robin problem driven by a nonlinear nonhomogeneous differential operator and with a superlinear Carathéodory reaction term. We prove a bifurcation-type theorem for small values of the parameter. Also, we show that as the parameter {\lambda>0} approaches zero, we can find positive solutions with arbitrarily big and arbitrarily small Sobolev norm. Finally, we show that for every admissible parameter value, there is a smallest positive solution {u^{*}_{\lambda}} of the problem, and we investigate the properties of the map {\lambda\mapsto u^{*}_{\lambda}}.

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32

Ghosh, S. S., A. Sen, and G. S. Lakhina. "Parametric Variations of Dromion Solutions in Auroral Plasmas." IEEE Transactions on Plasma Science 32, no. 3 (2004): 1367–77. http://dx.doi.org/10.1109/tps.2004.830544.

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33

Couto, Oliver, and Seiji Tomita. "Generalized Parametric Solutions to Multiple Sums of Powers." Universal Journal of Applied Mathematics 3, no. 5 (2015): 102–11. http://dx.doi.org/10.13189/ujam.2015.030503.

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34

Zhang, Lei, Anfu Zhu, Aiguo Wu, and Lingling Lv. "Parametric solutions to the regulator-conjugate matrix equations." Journal of Industrial & Management Optimization 13, no. 2 (2017): 623–31. http://dx.doi.org/10.3934/jimo.2016036.

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35

González, D., J. V. Aguado, E. Cueto, E. Abisset-Chavanne, and F. Chinesta. "kPCA-Based Parametric Solutions Within the PGD Framework." Archives of Computational Methods in Engineering 25, no. 1 (2016): 69–86. http://dx.doi.org/10.1007/s11831-016-9173-4.

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36

Brumelle, Shelby, Daniel Granot, and Li Liu. "Ordered optimal solutions and parametric minimum cut problems." Discrete Optimization 2, no. 2 (2005): 123–34. http://dx.doi.org/10.1016/j.disopt.2005.03.002.

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37

Fiacco, Anthony V., and Jerzy Kyparisis. "Computable bounds on parametric solutions of convex problems." Mathematical Programming 40-40, no. 1-3 (1988): 213–21. http://dx.doi.org/10.1007/bf01580732.

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38

GASIŃSKI, Leszek, and Nikolaos S. PAPAGEORGIOU. "Positive solutions for parametric equidiffusive p-Laplacian equations." Acta Mathematica Scientia 34, no. 3 (2014): 610–18. http://dx.doi.org/10.1016/s0252-9602(14)60033-3.

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39

Papageorgiou, Nikolaos S., Vicenţiu D. Rădulescu, and Dušan D. Repovš. "Positive solutions for nonlinear parametric singular Dirichlet problems." Bulletin of Mathematical Sciences 09, no. 03 (2019): 1950011. http://dx.doi.org/10.1142/s1664360719500115.

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We consider a nonlinear parametric Dirichlet problem driven by the [Formula: see text]-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ([Formula: see text])-linear near [Formula: see text]. The problem is uniformly nonresonant with respect to the principal eigenvalue of [Formula: see text]. We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter [Formula: see text].

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40

Rao, Murali, and Jan Sokolowski. "Differential stability of solutions to parametric optimization problems." Mathematical Methods in the Applied Sciences 14, no. 4 (1991): 281–94. http://dx.doi.org/10.1002/mma.1670140405.

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41

Huy, N. Q., and G. M. Lee. "Sensitivity of Solutions to a Parametric Generalized Equation." Set-Valued Analysis 16, no. 7-8 (2008): 805–20. http://dx.doi.org/10.1007/s11228-008-0094-8.

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42

Khanh, P. Q., and D. T. Luc. "Stability of Solutions in Parametric Variational Relation Problems." Set-Valued Analysis 16, no. 7-8 (2008): 1015–35. http://dx.doi.org/10.1007/s11228-008-0101-0.

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43

Moitra, Ayan, Christopher Chabalko, and Balakumar Balachandran. "Extreme wave solutions: Parametric studies and wavelet analysis." International Journal of Non-Linear Mechanics 83 (July 2016): 39–47. http://dx.doi.org/10.1016/j.ijnonlinmec.2016.03.011.

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44

Bolte, Jérôme, Edouard Pauwels, and Antonio Silveti-Falls. "Differentiating Nonsmooth Solutions to Parametric Monotone Inclusion Problems." SIAM Journal on Optimization 34, no. 1 (2024): 71–97. http://dx.doi.org/10.1137/22m1541630.

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45

Bougoffa, Lazhar, Smail Bougouffa, and Ammar Khanfer. "Approximate and Parametric Solutions to SIR Epidemic Model." Axioms 13, no. 3 (2024): 201. http://dx.doi.org/10.3390/axioms13030201.

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This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robust

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46

Han, Shaoning, and Jong-Shi Pang. "Continuous Selections of Solutions to Parametric Variational Inequalities." SIAM Journal on Optimization 34, no. 1 (2024): 870–92. http://dx.doi.org/10.1137/22m1514982.

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47

Lv, Lingling, Shiyu Tang, and Lei Zhang. "Parametric solutions to generalized periodic Sylvester bimatrix equations." Journal of the Franklin Institute 357, no. 6 (2020): 3601–21. http://dx.doi.org/10.1016/j.jfranklin.2019.12.031.

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48

LI, JIBIN, JIANHONG WU, and HUAIPING ZHU. "TRAVELING WAVES FOR AN INTEGRABLE HIGHER ORDER KDV TYPE WAVE EQUATIONS." International Journal of Bifurcation and Chaos 16, no. 08 (2006): 2235–60. http://dx.doi.org/10.1142/s0218127406016033.

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Using the method of planar dynamical systems to a higher order wave equations of KdV type, the existence of smooth and nonsmooth solitary wave, kink wave and uncountably infinite many periodic wave solutions is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some spatial conditions, the exact explicit parametric representations of solitary wave solutions are determined.

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49

Yong, Y., and Y. K. Lin. "Exact Stationary-Response Solution for Second Order Nonlinear Systems Under Parametric and External White-Noise Excitations." Journal of Applied Mechanics 54, no. 2 (1987): 414–18. http://dx.doi.org/10.1115/1.3173029.

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Except for rare sporadic cases, exact stationary solutions for second order nonlinear systems under Gaussian white-noise excitations are known only for certain types of systems and only when the excitations are purely external (additive). Yet, in many engineering problems, random excitations may also be parametric (multiplicative). It is shown in this paper that the method of detailed balance developed by the physicists can be applied to obtain systematically the stationary solutions for a large class of nonlinear systems under either external random excitations or parametric random excitation

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50

Shperberg, Shahaf S., Ariel Felner, Nathan R. Sturtevant, Solomon E. Shimony, and Avi Hayoun. "Enriching Non-Parametric Bidirectional Search Algorithms." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 2379–86. http://dx.doi.org/10.1609/aaai.v33i01.33012379.

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NBS is a non-parametric bidirectional search algorithm proven to expand at most twice the number of node expansions required to verify the optimality of a solution. We introduce new variants of NBS that are aimed at finding all optimal solutions. We then introduce an algorithmic framework that includes NBS as a special case. Finally, we introduce DVCBS, a new algorithm in this framework that aims to further reduce the number of expansions. Unlike NBS, DVCBS does not have any worst-case bound guarantees, but in practice it outperforms NBS in verifying the optimality of solutions.

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