Algebraic traveling wave solutions, Darboux polynomials and polynomial solutions

DOI10.1007/s12346-017-0245-0zbMath1407.34042OpenAlexW2732485477MaRDI QIDQ1617225

Claudia Valls

Publication date: 7 November 2018

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-017-0245-0

zbMATH Keywords

travelling wavepolynomial solutionDarboux polynomialKolmogorov-Petrovskii-Piskunov equationpolynomial linear equationZeldovich equation

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Traveling wave solutions (35C07)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Algebraic traveling waves for the generalized Newell-Whitehead-Segel equation
• New periodic and soliton wave solutions for the generalized Zakharov system and \((2 + 1)\)-dimensional Nizhnik-Novikov-Veselov system
• New applications of developed Jacobi elliptic function expansion methods
• The homotopy perturbation method for nonlinear oscillators with discontinuities.
• Complete characterization of algebraic traveling wave solutions for the Boussinesq, Klein-Gordon and Benjamin-Bona-Mahony equations
• An improved algebra method and its applications in nonlinear wave equations
• Travelling waves in nonlinear diffusion-convection reaction
• Exact solutions for a compound KdV-Burgers equation
• Algebraic traveling waves for some family of reaction-diffusion equations including the Nagumo equations
• New solitary wave solutions for the bad Boussinesq and good Boussinesq equations
• NEW SOLITONS AND PERIODIC SOLUTIONS FOR THEKADOMTSEV-PETVIASHVILI EQUATION
• Explicit travelling waves and invariant algebraic curves
• Finite bandwidth, finite amplitude convection
• Symmetries and differential equations