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Abstract
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
Highlights
The study of N = 2 supersymmetric (SUSY) extensions of nonlinear evolution equations has been largely studied in the past [1,2,3,4,5,6,7,8] in terms of integrability conditions and solutions
We show that some of these extensions can be related to a linear partial differential equation (PDE) by assuming that A is a chiral superfield [9]
It is well known [13,14,16,17,18,19] that we can generate via the Hirota bilinear formalism N soliton and similarity solutions in the classical case and in SUSY N = 1 extensions
Summary
The study of N = 2 supersymmetric (SUSY) extensions of nonlinear evolution equations has been largely studied in the past [1,2,3,4,5,6,7,8] in terms of integrability conditions and solutions Such extensions are given as a Grassmann-valued partial differential equation with one dependent variable A(x, t; θ1 , θ2 ). Vries [1] (SKdVa ), modified Korteweg–de Vries [6] (SmKdV) and Burgers [5] (SB) equations from a chiral superfield point of view In this instance, the equations, in terms of the complex covariant derivatives Equation (3), reads, respectively, as.
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