Interactions of breathers and kink pairs of the double sine-Gordon equation

DOI10.1134/S0965542514120112zbMath1327.65199OpenAlexW2027035125MaRDI QIDQ889210

S. P. Popov

Publication date: 6 November 2015

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542514120112

zbMATH Keywords

numerical exampleRunge-Kutta methodsine-Gordon equationdouble sine-Gordon equationantikinkbreatherkinkkink-anti-kink interactionquasi-spectral Fourier method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) PDEs in connection with quantum mechanics (35Q40) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (7)

Kink excitation spectra in the \((1+1)\)-dimensional \(\phi^{8}\) model ⋮ Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model ⋮ Kink-antikink collisions in the periodic \(\varphi^4\) model ⋮ Analytic solutions for the (2+1)-dimensional generalized sine-Gordon equations in nonlinear optics ⋮ BIFURCATION ANALYSIS AND EXACT TRAVELING WAVE SOLUTIONS FOR A GENERIC TWO-DIMENSIONAL SINE-GORDON EQUATION IN NONLINEAR OPTICS ⋮ Head butting sheep: kink collisions in the presence of false vacua ⋮ Solitons in complex systems of chiral fields with Kuramoto interactions

Cites Work

• Interaction properties of the periodic and step-like solutions of the double-sine-Gordon equation
• New interaction solutions of multiply periodic, quasi-periodic and non-periodic waves for the \((n+1)\)-dimensional double sine-Gordon equations
• Quantum vacuum interaction between two sine-Gordon kinks
• Generalized sine-Gordon solitons
• The sine-Gordon wobble
• Perturbed soliton solutions of the sine-Gordon equation

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