Singular solutions for the fourth‐order parabolic equation with nonstandard growth conditions and absorption

Abstract

This paper deals with the fourth-order parabolic equation u t + Δ 2 u = 𝜇u p(x) − 𝜆u q(x) in a bounded domain, subject to homogeneous Navier boundary conditions. Under some conditions on the variable exponents, we give a complete and optimal classification on the singularity of solutions, characterized by the signs of the Nehari energy and the difference between the initial energy and the potential depth.

Dynamical behaviors, chaotic pattern, phase portraits and multiple optical solitons for coupled stochastic Schrödinger-Hirota system in magneto-optic waveguides with multiplicative white noise via Itô calculus

“…In different cases, there are various aspects and corrections that make soliton dynamics promising, whether in fluid dynamics, quantum optics, or even nuclear physics or plasma physics. Over the years, many of researchers and scholars concerned in their papers on constructing optical solitons solutions and traveling wave solutions for a range of nonlinear evolution equations (NLEEs) model by means of different methods [1][2][3][4][5][6][7][8][9][10][11].…”