Soliton excitations and interaction in alpha helical protein with interspine coupling in modified nonlinear Schrodinger equation

The three-coupling modified nonlinear Schr?dinger(MNLS) equation with variable-coefficients is used to describe the dynamics of soliton in alpha helical protein. This MNLS equation with variable-coefficients is firstly transformed to the MNLS equation with constant-coefficients by similarity transformation. And then the one-soliton and two-soliton solutions of the variable-coefficient-MNLS equation are obtained by solving the constant-coefficient-MNLS equation with Hirota method. The effects of different parameter conditions on the soliton solutions are discussed in detail. The interaction between two solitons is also discussed. Our results are helpful to understand the soliton dynamics in alpha helical protein.

Multi-soliton solutions for the coupled modified nonlinear Schrdinger equations via Riemann–Hilbert approach

The coupled modified nonlinear Schrodinger equations are under investigation in this work. Starting from analyzing the spectral problem of the Lax pair, a Riemann-Hilbert problem for the coupled modified nonlinear Schrodinger equations is formulated. And then, through solving the obtained Riemann-Hilbert problem under the conditions of irregularity and reflectionless case, N-soliton solutions for the equations are presented. Furthermore, the localized structures and dynamic behaviors of the one-soliton solution are shown graphically.

New Exact Traveling Wave Solutions of the Unstable Nonlinear Schrdinger Equations

The present paper studies the unstable nonlinear Schr¨odinger equations, describing the time evolution of disturbances in marginally stable or unstable media. More precisely, the unstable nonlinear Schr¨odinger equation and its modified form are analytically solved using two efficient distinct techniques, known as the modified Kudraysov method and the sine-Gordon expansion approach. As a result, a wide range of new exact traveling wave solutions for the unstable nonlinear Schr¨odinger equation and its modified form are formally obtained.

On a Class of Quasilinear Elliptic Equations

We consider a class of quasilinear elliptic boundary problems,including the following Modified Nonlinear Schrödinger Equation as a special case:{Δu+1/2 uΔ(u^(2))−V(x)u+|u|^(q−2)u=0 in Ω,u=0 on∂Ω,whereΩis the entire space R^(N) orΩ⊂R^(N) is a bounded domain with smooth boundary,q∈(2,22^(∗)]with 2^(∗)=2 N/(N−2)being the critical Sobolev exponent and 22^(∗)=4 N/(N−2).We review the general methods developed in the last twenty years or so for the studies of existence,multiplicity,nodal property of the solutions within this range of nonlinearity up to the new critical exponent 4 N/(N−2),which is a unique feature for this class of problems.We also discuss some related and more general problems.