相关论文: Nonlinear von Neumann-type equations
This paper considers a pair of coupled nonlinear Helmholtz equations \begin{align*} -\Delta u - \mu u = a(x) \left( |u|^\frac{p}{2} + b(x) |v|^\frac{p}{2} \right)|u|^{\frac{p}{2} - 2}u, \end{align*} \begin{align*} -\Delta v - \nu v = a(x)…
A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux…
The von Neumann equation with delta self-interaction kernel serves as a statistical model for nonlinear waves, and it exhibits a bifurcation between stable and unstable regimes. In oceanography it is known as the Alber equation, and its…
The Koopman--von Neumann equation describes the evolution of a complex-valued wavefunction corresponding to the probability distribution given by an associated classical Liouville equation. Typically, it is defined on the whole Euclidean…
A new integrable system of two symmetrically coupled derivative nonlinear Schroedinger equations is detected by means of the singularity analysis. A nonlinear transformation is proposed which uncouples the equations of the new system.
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
Darboux transformation is developed to systematically find variable separation solutions for the Nizhnik-Novikov-Veselov equation. Starting from a seed solution with some arbitrary functions, the once Darboux transformation yields the…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative…
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous…
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber…
The hierarchy of integrable equations are considered. The dynamical approach to the theory of nonlinear waves is proposed. The special solutions(nonlinear waves) of considered equations are derived. We use powerful methods of computer…
We consider meromorphic particular solutions of nonlinear ordinary differential equations and perform a perturbation {\it \`a la} Poincar\'e making their linearized equation non-Fuchsian at the movable pole and Fuchsian at infinity. When…
We address the open problem of existence of singularities for the complex Ginzburg-Landau equation. Using a combination of rigourous results and numerical computations, we describe a countable family of self-similar singularities. Our…
In this paper, we prove some Liouville theorem for the following elliptic equations involving nonlocal nonlinearity and nonlocal boundary value condition $$ \left\{ \begin{array}{ll} \displaystyle -\Delta u(y)=\intpr \frac{…