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Explicit Solutions of the Nonlinear Schrödinger-Type Equation
In this work, we focus on the construction of explicit solutions of the nonlinear Schrödinger-type equation, which has various applications in...
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Mixed Problem for a Nonlinear Parabolic Equation with Involution
AbstractIn this paper, we consider a nonlinear parabolic differential equation with involution. With respect to spatial variable is used Dirichlet...
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Nonlinear Perturbed BLMP Equation
In the present paper we consider the non-existence of weak solutions related to a class of differential equations connected with the Airy operator....
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The Cauchy Problem for a Doubly Nonlinear Parabolic Equation with Variable Density and Nonlinear Time-Dependent Absorption
Based on a self-similar analysis of the Fujita type global solvability, we obtain estimates for a solution and fronts (a free boundary) of the Cauchy...
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Optical Solitons of Nonlinear Schrödinger Equation with Anomalous Dispersion Regime
AbstractIn this study, the optical solitons of nonlinear Schrödinger equation with anomalous dispersion are investigated via Improved Bernoulli...
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Breather Transitions and Their Mechanisms of a (2+1)-Dimensional Sine-Gordon Equation and a Modified Boussinesq Equation in Nonlinear Dynamics
Studying the transformation mechanisms of soliton solutions of some high-dimensional equations can aid in comprehending the physical phenomena of the...
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Exact Solutions for the Fractional Nonlinear Boussinesq Equation
We investigate the existence of exact solutions in closed form to a fractional version of the nonlinear Boussinesq equation for groundwater flow...
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Boundary Value Problems for a Parabolic-Hyperbolic Equation with Nonlinear Loaded Terms
AbstractIn the present work local and nonlocal boundary value problem involves nonlinear gluing condition for a loaded parabolic-hyperbolic type...
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Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation
Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the...
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Nonlinear Schrödinger Equation with Delay and Its Regularization
AbstractThe properties of an initial-boundary value problem for a nonlinear Schödinger equation including terms with a delay of the time argument in...
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On a Nonlinear Second-Order Ordinary Differential Equation
AbstractWe consider a nonlinear second-order ordinary differential equation of a special form whose particular case arises when constructing exact...
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Solving A Nonlinear Equation
In this chapter, one of the more common mathematical problems is studied, which is to find the solution, or solutions, of an equation of the form...
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Inverse Problems for the Higher Order Nonlinear Schrödinger Equation
The results on the well-posedness of inverse problems with integral overdetermination on a bounded interval for the higher order nonlinear...
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The Daugavet Equation: Linear and Nonlinear Recent Results
A bounded linear operator \( T:\mathcal{X}\to \mathcal{X} \)...
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Nonlinear Schrödinger Approximation for the Electron Euler-Poisson Equation
The nonlinear Schrödinger (NLS for short) equation plays an important role in describing slow modulations in time and space of an underlying...
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A new nonlinear compact difference scheme for a fourth-order nonlinear Burgers type equation with a weakly singular kernel
In this study, we propose a new nonlinear compact difference scheme (NCDS) for a fourth-order nonlinear Burgers type equation (FO-NBTE) with a weakly...
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Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schrödinger equation
In this manuscript, our primary objective is to delve into the intricacies of an extended nonlinear Schrödinger equation. To achieve this, we...
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Time-weighted estimates for the Blackstock equation in nonlinear ultrasonics
High frequencies at which ultrasonic waves travel give rise to nonlinear phenomena. In thermoviscous fluids, these are captured by Blackstock’s...
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Identification of source term in a nonlinear degenerate parabolic equation with memory
In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To...
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Convergence of linear and nonlinear Neumann–Neumann method for the Cahn–Hilliard equation
In this paper, we propose and analyze a non-overlap** substructuring type algorithm for the Cahn–Hilliard equation. Being a nonlinear equation, it...
