Solitary waves for the perturbed nonlinear Klein-Gordon equation

Abstract In this work, we study the perturbed nonlinear Klein–Gordon equation. We shall use the sech-ansatze method to derive the solitary wave solutions of this equation.

[1]  Anjan Biswas,et al.  1-Soliton solution of the B(m,n) equation with generalized evolution , 2009 .

[2]  T. Nishida,et al.  A mathematical justification for Korteweg-de Vries equation and Boussinesq equation of water surface waves , 1986 .

[3]  N. Berloff,et al.  Nonlinear Wave Interactions in Nonlinear Nonintegrable Systems , 1998 .

[4]  M. Ablowitz,et al.  Solitons, Nonlinear Evolution Equations and Inverse Scattering , 1992 .

[5]  Howard A. Levine,et al.  Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations , 1974 .

[6]  A. Darwish,et al.  Applications of algebraic method to exactly solve some nonlinear partial differential equations , 2007 .

[7]  Anjan Biswas,et al.  Topological and non-topological solitons of the generalized Klein-Gordon equations , 2009, Appl. Math. Comput..

[8]  G. M.,et al.  A Treatise on the Mathematical Theory of Elasticity , 1906, Nature.

[9]  Nikolai A. Kudryashov,et al.  On types of nonlinear nonintegrable equations with exact solutions , 1991 .

[10]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[11]  Anjan Biswas,et al.  Solitary waves of Boussinesq equation in a power law media , 2009 .

[12]  広田 良吾,et al.  The direct method in soliton theory , 2004 .

[13]  Darryl D. Holm,et al.  Stepwise Precession of the Resonant Swinging Spring , 2001, SIAM J. Appl. Dyn. Syst..

[14]  Abdul-Majid Wazwaz,et al.  Generalized forms of the phi-four equation with compactons, solitons and periodic solutions , 2005, Math. Comput. Simul..

[15]  Alan C. Lazer,et al.  Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis , 1990, SIAM Rev..

[16]  S. Levandosky.  Stability and Instability of Fourth-Order Solitary Waves , 1998 .

[17]  Abdul-Majid Wazwaz,et al.  Variants of the two-dimensional boussinesq equation with compactons, solitons, and periodic solutions , 2005 .

[18]  Abdul-Majid Wazwaz,et al.  New travelling wave solutions to the Boussinesq and the Klein–Gordon equations , 2008 .

[19]  J. E. Lin.  LOCAL TIME DECAY FOR A NONLINEAR BEAM EQUATION , 2005 .

[20]  Engui Fan,et al.  Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method , 2002 .

[21]  V. G. Makhankov,et al.  Dynamics of classical solitons (in non-integrable systems) , 1978 .

[22]  Kurt M. Berger,et al.  Simulation of Wave Interactions and Turbulence in One-Dimensional Water Waves , 2003, SIAM J. Appl. Math..

[23]  M. Ablowitz,et al.  The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .

[24]  Francis P. Bretherton,et al.  Resonant interactions between waves. The case of discrete oscillations , 1964, Journal of Fluid Mechanics.

[25]  S. Levandosky.  Decay Estimates for Fourth Order Wave Equations , 1998 .

[26]  A. Elgarayhi,et al.  New periodic wave solutions for the shallow water equations and the generalized Klein–Gordon equation , 2008 .

[27]  R. Hirota,et al.  N-Soliton Solutions of Model Equations for Shallow Water Waves , 1976 .

[28]  W. Walter,et al.  Nonlinear oscillations in a suspension bridge , 1987 .

[29]  A. Biswas,et al.  Topological and non-topological solitons of the Klein–Gordon equations in 1+2 dimensions , 2010 .

[30]  S. Levandosky,et al.  Time decay for the nonlinear beam equation , 2000 .

[31]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[32]  G. Galdi.  Non-linear stability of the magnetic Bénard problem via a generalized energy method , 1985 .

[33]  Abdul-Majid Wazwaz,et al.  The tanh and the sine-cosine methods for compact and noncompact solutions of the nonlinear Klein-Gordon equation , 2005, Appl. Math. Comput..

[34]  Filipe J. Romeiras.  Exact travelling wave solutions of the generalized Bretherton equation , 2009, Appl. Math. Comput..