Lorentzian Solitary Wave in a Generalised Nonlinear Schrödinger Equation

Abstract

We obtain a travelling-wave solution of a generalised nonlinear Schrödinger equation with an additional term of the form $\Gamma (\psi (x,t))=\lambda \psi (x,t{)}^q$, where $\lambda$ and $q$ are real constants. Moreover, we show that the density of energy of the system for the travelling-wave solution presents a Lorentzian solitary wave behaviour.

arXiv comment9 pages. To appear in Physics Letters A

References in corpus (9)

• Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
• Nonlinear Schroedinger Equation in the Presence of Uniform Acceleration
• Possible Divergences in Tsallis' Thermostatistics
• From the hypergeometric differential equation to a non linear Schrödinger one
• Solutions for a q-generalized Schrödinger equation of entangled interacting particles
• Dissipative Effects in Nonlinear Klein-Gordon Dynamics
• Generalized Nonlinear Proca Equation and its Free-Particle Solutions
• Tsallis' Quantum q-Fields
• Classical and \textcolor{blue}{Quantum} Field-Theoretical approach to the non-linear q-Klein-Gordon Equation

Cited by in corpus (3)

• Deformed Fokker-Planck equation: inhomogeneous medium with a position-dependent mass
• Generalized and new solutions of the NRT nonlinear Schrödinger equation
• A Nonlinear $q$-Deformed Schrödinger Equation