Something hidden in the Fourier series and its partial sum: Solitary wave solutions to polynomial nonlinear differential equations

DOI10.1016/S0165-2125(97)00025-5zbMath0917.35116MaRDI QIDQ1276624

Chuntao Yan

Publication date: 5 August 1999

Published in: Wave Motion (Search for Journal in Brave)

zbMATH Keywords

Burgers equationnonlinear Schrödinger equationKdV equationsine-Gordon equationtraveling wave solutionspolynomial nonlinear evolution equationspolynomial solitary waves

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Soliton equations (35Q51)

Related Items

A simple transformation for nonlinear waves. ⋮ The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations ⋮ A new formulation of the general solution to Burgers' equation.

Uses Software

• MACSYMA

Cites Work

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• Exact solutions to the Korteweg-de Vries-Burgers equation
• An analytic solution of Burgers-KdV equation
• Who cares about integrability?
• The Korteweg-de Vries-Burgers' equation: A reconstruction of exact solutions
• Exact solutions to the KdV--Burgers' equation
• KdV-Burgers equation modelling of turbulence
• The use of Borel-summation in the establishment of non-existence of certain travelling-wave solutions of the Kuramoto-Sivashinsky equation
• Bäcklund transformations, truncated Painlevé expansions, and special solutions of nonintegrable long-wave evolution equations
• A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
• Solitary waves on nonlinear elastic rods. I
• Travelling-wave solutions to the Korteweg-de Vries-Burgers equation
• On the Inverse Scattering Problem for Cubic Eigenvalue Problems of the Class ψ_xxx + 6Qψ_x + 6R_ψ = λψ
• Analytic solutions of the Nagumo equation
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries
• Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA
• Traveling wave solutions of nonlinear partial differential equations