A numerical scheme and some theoretical aspects for the cylindrically and spherically symmetric sine-Gordon equations

DOI10.1016/j.cnsns.2015.12.008zbMath1470.65154OpenAlexW2217500501MaRDI QIDQ2198854

Lu Trong Khiem Nguyen

Publication date: 15 September 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2015.12.008

zbMATH Keywords

predictor-correctorreturning effectring waveslope modulation

Mathematics Subject Classification ID

Nonlinear waves in solid mechanics (74J30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Soliton equations (35Q51) Modulation and demodulation in information and communication theory (94A14) Second-order semilinear hyperbolic equations (35L71)

Related Items

An efficient finite difference/Hermite-Galerkin spectral method for time-fractional coupled sine-Gordon equations on multidimensional unbounded domains and its application in numerical simulations of vector solitons ⋮ Higher order scheme for two-dimensional inhomogeneous sine-Gordon equation with impulsive forcing ⋮ Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations ⋮ A compact difference scheme for a two dimensional nonlinear fractional Klein-Gordon equation in polar coordinates ⋮ Padé numerical schemes for the sine-Gordon equation ⋮ Modulation theory for radially symmetric kink waves governed by a multi-dimensional sine-Gordon equation

Cites Work

• Unnamed Item
• Unnamed Item
• Slope modulation of waves governed by sine-Gordon equation
• A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions
• An approach to radially symmetrical solutions of the sine-Gordon equation
• Decay of shrinking solitons in multidimensional sine-Gordon equation
• Bäcklund transformations and new solutions of nonlinear wave equations in four-dimensional space-time
• Evolution of lump solutions for the KP equation
• Solitary wave evolution for mKdV equations
• Evolution of two-dimensional standing and travelling breather solutions for the sine-Gordon equation
• The solution of the two-dimensional sine-Gordon equation using the method of lines
• Slope modulation of ring waves governed by two-dimensional sine-Gordon equation
• Two-timing, variational principles and waves
• Bäcklund transformations for multidimensional sine-Gordon equations
• Ring-Shaped Quasi-Soliton Solutions to the Two- and Three-Dimensional Sine-Gordon Equation
• A general approach to linear and non-linear dispersive waves using a Lagrangian
• Pulse evolution for a two-dimensional sine-Gordon equation
• Approximate evolution of lump initial conditions for the Benjamin-Ono equation.