Toward a classification of quasirational solutions of the nonlinear Schrödinger equation

DOI10.1134/S0040577916100044zbMath1355.76016MaRDI QIDQ508928

Yong-Cai Geng, Sumit K. Garg

Publication date: 8 February 2017

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

zbMATH Keywords

nonlinear Schrödinger equationdeterminantrogue wavePeregrine breather

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Shock waves and blast waves in fluid mechanics (76L05) Solitary waves for incompressible inviscid fluids (76B25) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton solutions (35C08)

Related Items (1)

Degenerate Riemann theta functions, Fredholm and Wronskian representations of the solutions to the KdV equation and the degenerate rational case

Cites Work

• The Peregrine breather of order nine and its deformations with sixteen parameters solutions to the NLS equation
• Exact first-order solutions of the nonlinear Schrödinger equation
• Two parameters wronskian representation of solutions of nonlinear Schrödinger equation, eighth Peregrine breather and multi-rogue waves
• Water waves, nonlinear Schrödinger equations and their solutions
• Families of quasi-rational solutions of the NLS equation and multi-rogue waves
• Lie symmetries of a generalised nonlinear Schrodinger equation: I. The symmetry group and its subgroups
• Lie symmetries of a generalised non-linear Schrodinger equation. II. Exact solutions
• Lie symmetries of a generalised non-linear Schrodinger equation. III. Reductions to third-order ordinary differential equations
• Rogue waves, rational solutions, the patterns of their zeros and integral relations
• TRIP
• Other 2N− 2 parameters solutions of the NLS equation and 2N+ 1 highest amplitude of the modulus of theNth order AP breather
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation
• Degenerate determinant representation of solutions of the nonlinear Schrödinger equation, higher order Peregrine breathers and multi-rogue waves
• Six-parameters deformations of fourth order Peregrine breather solutions of the nonlinear Schrödinger equation
• The Fifth Order Peregrine Breather and Its Eight-Parameter Deformations Solutions of the NLS Equation
• Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability

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