Dynamics of interaction between lumps and solitons in the Mel'nikov equation
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Publication:2213879
DOI10.1016/j.cnsns.2020.105429zbMath1448.35437OpenAlexW3037151591MaRDI QIDQ2213879
Jiguang Rao, Boris A. Malomed, Jing-Song He, Yi. Cheng
Publication date: 3 December 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.2020.105429
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)
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Cites Work
- Unnamed Item
- Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation
- Nonlinear fast growth of water waves under wind forcing
- On equations for wave interactions
- Solitons and infinite dimensional Lie algebras
- Bilinear transformation method
- A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x,y plane
- Exponentially localized solutions of Mel'nikov equation
- Painléve analysis and Bäcklund transformations for coupled generalized Schrödinger-Boussinesq system
- On the solution of the coupled Schrödinger-KdV equation by the decomposition method
- Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
- Degeneration of breathers in the Kadomttsev-Petviashvili I equation
- Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
- Two spatial dimensional N-rogue waves and their dynamics in Mel'nikov equation
- Integrable multidimensional versions of the nonlocal nonlinear Schrödinger equation
- General N-Dark-Dark Solitons in the Coupled Nonlinear Schrödinger Equations
- Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions
- The modulational instability in deep water under the action of wind and dissipation
- Reflection of waves in nonlinear integrable systems
- Inverse scattering transform for the KPI equation on the background of a one-line soliton*
- Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method
- Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
- Dynamics of lumps and dark–dark solitons in the multi-component long-wave–short-wave resonance interaction system
- Transformations between Nonlocal and Local Integrable Equations
- Rogue waves of the nonlocal Davey–Stewartson I equation
- Integrable Nonlocal Nonlinear Equations
- Rational and Semirational Solutions of the Nonlocal Davey–Stewartson Equations
- Semi-rational solutions of the third-type Davey-Stewartson equation
- 𝓟𝓣-symmetric quantum mechanics
- Dynamics of rogue waves in the Davey–Stewartson II equation
- General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
- Multi-soliton energy transport in anharmonic lattices
- Interaction of lumps with a line soliton for the DSII equation
