P. G. Estevez, C. Qu, “Separation of Variables in a Nonlinear Wave Equation with a Variable Wave Speed”, TMF, 133:2 (2002), 202–210; Theoret. and Math. Phys., 133:2 (2002), 1490

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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 133, Number 2, Pages 202–210
DOI: https://doi.org/10.4213/tmf390 (Mi tmf390)

This article is cited in 23 scientific papers (total in 23 papers)

Separation of Variables in a Nonlinear Wave Equation with a Variable Wave Speed

P. G. Estevez^a, C. Qu^b

^a University of Salamanca
^b Northwest University

Full-text PDF (179 kB) Citations (23)

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DOI: https://doi.org/10.4213/tmf390

Abstract: We develop a generalized conditional symmetry approach for the functional separation of variables in a nonlinear wave equation with a nonlinear wave speed. We use it to obtain a number of new

(1 + 1)

$(1+1)$ -dimensional nonlinear wave equations with variable wave speeds admitting a functionally separable solution. As a consequence, we obtain exact solutions of the resulting equations.

Keywords: Lie symmetries, generalized symmetries, diffusion equations, nonlinear equations.

English version:
Theoretical and Mathematical Physics, 2002, Volume 133, Issue 2, Pages 1490–1497
DOI: https://doi.org/10.1023/A:1021190509331

Bibliographic databases:

Language: Russian

Citation: P. G. Estevez, C. Qu, “Separation of Variables in a Nonlinear Wave Equation with a Variable Wave Speed”, TMF, 133:2 (2002), 202–210; Theoret. and Math. Phys., 133:2 (2002), 1490–1497

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf390

https://doi.org/10.4213/tmf390

https://www.mathnet.ru/eng/tmf/v133/i2/p202

This publication is cited in the following 23 articles:

Daniel Arrigo, Synthesis Lectures on Mathematics & Statistics, Analytical Methods for Solving Nonlinear Partial Differential Equations, 2022, 149
Aksenov A.V., Polyanin A.D., “Methods For Constructing Complex Solutions of Nonlinear Pdes Using Simpler Solutions”, Mathematics, 9:4 (2021), 345
Zhurov I A., Polyanin A.D., “Symmetry Reductions and New Functional Separable Solutions of Nonlinear Klein-Gordon and Telegraph Type Equations”, J. Nonlinear Math. Phys., 27:2 (2020), 227–242
Polyanin A.D., “Functional Separation of Variables in Nonlinear Pdes: General Approach, New Solutions of Diffusion-Type Equations”, Mathematics, 8:1 (2020), 90
Polyanin A.D., Sorokin V.G., “New Exact Solutions of Nonlinear Wave Type Pdes With Delay”, Appl. Math. Lett., 108 (2020), 106512
Polyanin A.D., “Construction of Functional Separable Solutions in Implicit Form For Non-Linear Klein-Gordon Type Equations With Variable Coefficients”, Int. J. Non-Linear Mech., 114 (2019), 29–40
Polyanin A.D., “Comparison of the Effectiveness of Different Methods For Constructing Exact Solutions to Nonlinear Pdes. Generalizations and New Solutions”, Mathematics, 7:5 (2019), 386
Polyanin A.D., Zhurov A.I., “Functional Separable Solutions of Two Classes of Nonlinear Mathematical Physics Equations”, Dokl. Math., 99:3 (2019), 321–324
Daniel J. Arrigo, Synthesis Lectures on Mathematics & Statistics, Analytical Techniques for Solving Nonlinear Partial Differential Equations, 2019, 127
Peng X., Shang Ya., Zheng X., “New Non-Travelling Wave Solutions of Calogero Equation”, Adv. Appl. Math. Mech., 8:6 (2016), 1036–1049
Barannyk A.F., Barannyk T.A., Yuryk I.I., “Generalized Separation of Variables for Nonlinear Equation U(Tt) = F(U)U(XX) + Af `(U)U(X)(2)”, Rep. Math. Phys., 71:1 (2013), 1–13
Huang D.-jiang, Zhou Sh., “Group properties of generalized quasi-linear wave equations”, Journal of Mathematical Analysis and Applications, 366:2 (2010), 460–472
Wang, PZ, “Variable Separation for (1+1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives”, Communications in Theoretical Physics, 50:4 (2008), 797
Gou, M, “Functional separable solutions of nonlinear heat equations in non-Newtonian fluids”, Communications in Theoretical Physics, 49:2 (2008), 257
Zhang, SL, “Functional variable separation for extended nonlinear elliptic equations”, Communications in Theoretical Physics, 48:3 (2007), 385
Hu, JY, “Functionally separable solutions to nonlinear wave equations by group foliation method”, Journal of Mathematical Analysis and Applications, 330:1 (2007), 298
Hu, JY, “Functional separable solutions to nonlinear diffusion equations by group foliation method”, Communications in Theoretical Physics, 47:2 (2007), 193
Zhang, SL, “The derivative-dependent functional variable separation for the evolution equations”, Chinese Physics, 15:12 (2006), 2765
Zhang, SL, “Variable separation and exact separable solutions for equations of type u(xt) = A(u, u(x))u(xx)+B(u, u(x))”, Communications in Theoretical Physics, 45:6 (2006), 969
Zhang, SL, “Functional variable separation for extended (1+2)-dimensional nonlinear wave equations”, Chinese Physics Letters, 22:11 (2005), 2731

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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