Reflection of waves in nonlinear integrable systems

DOI10.1063/1.527752zbMath0663.35079OpenAlexW2380795121MaRDI QIDQ3812671

V. K. Mel'nikov

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527752

zbMATH Keywords

soliton solutionshydrodynamicsplasma physicsreflection of wavesnonlinear integrable systemssolid-state physicsinteraction of a long wave with a short wave packetSolutions of the boomeron type

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (13)

Capture and confinement of solitons in nonlinear integrable systems ⋮ New method for deriving nonlinear integrable systems ⋮ Families of rational and semirational solutions of the partial reverse space-time nonlocal Mel'nikov equation ⋮ Interaction of wave structure in the \(\mathcal{PT}\)-symmetric \((3+1)\)-dimensional nonlocal Mel'nikov equation and their applications ⋮ Dynamics of solitons and breathers on a periodic waves background in the nonlocal Mel'nikov equation ⋮ Dynamics of interaction between lumps and solitons in the Mel'nikov equation ⋮ Exponentially localized solutions of Mel'nikov equation ⋮ Bright and dark soliton solutions to the partial reverse space-time nonlocal Mel'nikov equation ⋮ Lump and mixed rogue-soliton solutions of the (2 + 1)-dimensional Mel'nikov system ⋮ Two spatial dimensional N-rogue waves and their dynamics in Mel'nikov equation ⋮ Interaction of lumps and dark solitons in the Mel'nikov equation ⋮ Homoclinic orbits for some \((2+1)\)-dimensional nonlinear Schrödinger-like equations ⋮ Nonclassical symmetry reductions of nonlinear partial differential equations

Cites Work

• On equations for wave interactions

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