New solitary wave solutions in a perturbed generalized BBM equation

DOI10.1007/s11071-019-05137-9zbMath1430.37088OpenAlexW2964339755WikidataQ127445150 ScholiaQ127445150MaRDI QIDQ2297015

Kun Zhu, Zanping Yu, Jianhe Shen, Yuhang Wu

Publication date: 18 February 2020

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-019-05137-9

zbMATH Keywords

solitary wavegeometric singular perturbation theoryBenjamin-Bona-Mahony equationMelnikov integral

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Singular perturbations in context of PDEs (35B25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Soliton solutions (35C08)

Related Items (8)

The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrödinger equation ⋮ Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method ⋮ Existence of periodic wave of a BBM equation with delayed convection and weak diffusion ⋮ Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity ⋮ Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion ⋮ Existence of traveling wave solutions for a generalized Burgers-Fisher equation with weak convection ⋮ On the existence of solitary wave solutions for perturbed Degasperis-Procesi equation ⋮ Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation

Cites Work

• Unnamed Item
• Existence of solitary waves and periodic waves for a perturbed generalized BBM equation
• Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers-KdV equation
• Solitary waves solutions of singularly perturbed higher-order KdV equation via geometric singular perturbation method
• Geometric singular perturbation theory for ordinary differential equations
• Global bifurcations and chaos. Analytical methods
• On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations
• Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation
• Exact solutions with compact and noncompact structures for the one-dimensional generalized Benjamin-Bona-Mahony equation
• The application of bifurcation method to a higher-order KdV equation
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• An integrable system with peakon, complex peakon, weak kink, and kink-peakon interactional solutions
• Geometric singular perturbation theory in biological practice
• Understanding Peakons, Periodic Peakons and Compactons via a Shallow Water Wave Equation
• A non-linear equation incorporating damping and dispersion
• Traveling waves in a generalized nonlinear dispersive–dissipative equation
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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