The two-dimensional Leznov lattice equation and its various solutions
DOI10.1016/j.physd.2023.133958OpenAlexW4388104680MaRDI QIDQ6198209
Ze-Lin Jin, Guo-Fu Yu, Han-Han Sheng, Bo-Jian Shen
Publication date: 21 February 2024
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2023.133958
algebraic solitonbreather solutionlump solutionKP-Toda reductiontwo-dimensional Leznov lattice equation
Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) 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) Lattice dynamics; integrable lattice equations (37K60) Soliton solutions (35C08)
Cites Work
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- Waves that appear from nowhere and disappear without a trace
- Rogue waves in the ocean
- Applying the Pfaffianization procedure to the two-dimensional Leznov lattice
- The structure of the rational solutions to the Boussinesq equation
- Graded Lie algebras, representation theory, integrable mappings and integrable systems
- Rogue waves in the nonlocal \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equation
- Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction
- Doubly localized two-dimensional rogue waves in the Davey-Stewartson I equation
- Rogue waves in the generalized derivative nonlinear Schrödinger equations
- Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy
- Rogue wave patterns in the nonlinear Schrödinger equation
- Pattern transformation in higher-order lumps of the Kadomtsev-Petviashvili I equation
- General breather and rogue wave solutions to the complex short pulse equation
- General rogue wave solution to the discrete nonlinear Schrödinger equation
- Multi-soliton solution to the two-component Hunter-Saxton equation
- Doubly localized rogue waves on a background of dark solitons for the Fokas system
- Rational solutions of a (2+1)-dimensional sinh-Gordon equation
- Lump solutions to the Kadomtsev-Petviashvili equation
- Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems
- Application of Hirota's bilinear formalism to a two-dimensional lattice by Leznov
- Solitons, breathers and rational solutions for a (2+1)-dimensional dispersive long wave system
- Kadomtsev-Petviashvili equation: one-constraint method and lump pattern
- Rogue waves in (2+1)-dimensional three-wave resonant interactions
- High-Order Solutions and Generalized Darboux Transformations of Derivative Nonlinear Schrödinger Equations
- Water waves, nonlinear Schrödinger equations and their solutions
- Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
- Integrable semi-discretizations and full-discretization of the two-dimensional Leznov lattice
- Two-dimensional lumps in nonlinear dispersive systems
- R-matrix approach to lattice integrable systems
- Method for Solving the Korteweg-deVries Equation
- Rogue waves of the nonlocal Davey–Stewartson I equation
- Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation
- General soliton solution to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions
- Some new results on the Blaszak–Marciniak lattice: Bäcklund transformation and nonlinear superposition formula
- Dynamics of rogue waves in the Davey–Stewartson II equation
- General rogue waves in the three-wave resonant interaction systems
- General soliton and (semi‐)rational solutions to the nonlocal Mel'nikov equation on the periodic background
- Rogue waves and lumps on the nonzero background in the ‐symmetric nonlocal Maccari system
- General rogue waves in the focusing and defocusing Ablowitz–Ladik equations
- General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
- Oceanic Rogue Waves
- Rogue waves and their patterns in the vector nonlinear Schrödinger equation