Solution for a non linear Schr\"odinger equation via Hopf-Cole transformation
H. R. Rezazadeh, Tirdad Soulati
TL;DR
This paper demonstrates that the one-dimensional nonlinear Schrödinger equation can be solved using a Hopf-Cole transformation, converting it into the Burgers equation, thus providing a novel analytical approach.
Contribution
The paper introduces a new method to solve the nonlinear Schrödinger equation by applying a Hopf-Cole transformation, linking it to turbulence models.
Findings
NLS can be transformed into Burgers equation using Hopf-Cole.
The transformation simplifies solving the nonlinear Schrödinger equation.
Provides a new analytical tool for nonlinear wave equations.
Abstract
In this short letter we show that the one dimensional non linear Schr\"odinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
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Taxonomy
TopicsNonlinear Waves and Solitons · Quantum Mechanics and Non-Hermitian Physics · Nonlinear Photonic Systems