Lump type solutions: Bäcklund transformation and spectral properties

PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Traveling wave solutions (35C07)

Cites Work

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The structure of the rational solutions to the Boussinesq equation
Solitary waves of generalized Kadomtsev-Petviashvili equations
Nonlinear stability of solitary waves of a generalized Kadomtsev-Petviashvili equation
Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation
A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
On the local and global well-posedness theory for the KP-I equation
Solutions of the Boussinesq equation
On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation
Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy
Pattern transformation in higher-order lumps of the Kadomtsev-Petviashvili I equation
Obliquely propagating skew KP lumps
Interaction of multi-lumps within the Kadomtsev-Petviashvili equation
Nondegeneracy, Morse index and orbital stability of the KP-I lump solution
Global well-posedness for the KP-I equation on the background of a non-localized solution
Two-dimensional lumps in nonlinear dispersive systems
Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution
Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves
Multiple branches of travelling waves for the Gross–Pitaevskii equation
Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
Lump Solutions for PDE's: Algorithmic Construction and Classification
RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION
Uniqueness of lump solution to the KP-I equation

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