\(N = 2\) \(a = 1\) supersymmetric KdV equation and its Darboux-Bäcklund transformations

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Cites Work

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Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation
Super quasiperiodic wave solutions and asymptotic analysis for \(\mathcal N=1\) supersymmetric KdV-type equations
Bilinear approach to \(N = 2\) supersymmetric KdV equations
A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy
The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems
Bäcklund-Darboux transformations and discretizations of \(N=2a=-2\) supersymmetric KdV equation
Solitary wave and doubly periodic wave solutions for the Kersten-Krasil'shchik coupled KdV-mKdV system
Darboux transformations for the supersymmetric two-boson hierarchy
Bäcklund-Darboux transformations and discretizations of super KdV equation
Nonlinear superposition formula for \(N=1\) supersymmetric KdV equation
Darboux transformations in integrable systems. Theory and their applications to geometry
Hirota bilinear form for the super-KdV hierarchy
Constructing the soliton solutions for the \(N=1\) supersymmetric KdV hierarchy
Discrete systems and integrability
Super extension of Bell polynomials with applications to supersymmetric equations
Supersymmetric KdV equation: Darboux transformation and discrete systems
A Note on Exact Traveling Wave Solutions of the Perturbed Nonlinear Schrödinger's Equation with Kerr Law Nonlinearity
Dynamical Analysis and Exact Solutions of a New (2+1)-Dimensional Generalized Boussinesq Model Equation for Nonlinear Rossby Waves*
A Supersymmetric AKNS Problem and Its Darboux‐Bäcklund Transformations and Discrete Systems
Supersymmetric extension of the Korteweg–de Vries equation
Bäcklund transformations and nonlinear differential difference equations
Nonlinear differential difference equations as Backlund transformations
A new N=2 supersymmetric Korteweg–de Vries equation
INTEGRABILITY AND BIHAMILTONIAN STRUCTURE OF THE EVEN ORDER SKDV HIERARCHIES
Extension of the bilinear formalism to supersymmetric KdV-type equations
Integrability of Kersten–Krasil’shchik coupled KdV–mKdV equations: singularity analysis and Lax pair
Bell Polynomial Approach and N -Soliton Solutions for a Coupled KdV-mKdV System

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