Related papers: Nonlinear self-adjointness and conservation laws

We establish sharp energy decay rates for a large class of nonlinearly first-order damped systems, and we design discretization schemes that inherit of the same energy decay rates, uniformly with respect to the space and/or time…

The nonlinear eigenvalue problem of a class of second order semi-transcendental differential equations is studied. A nonlinear eigenvalue is defined as the initial condition which gives rise a separatrix solution. A semi-transcendental…

A method based on infinite parameter conservation laws is described to factor linear differential operators out of nonlinear partial differential equations (PDEs) or out of differential consequences of nonlinear PDEs. This includes a…

We elaborate on the duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction…

It is shown that a hot relativistic fluid could be viewed as a collection of self-interacting quantum objects. They obey a nonlinear equation which is a modification of the quantum equation obeyed by elementary constituents of the fluid. A…

In this paper, we construct and analyse the symmetries and conservation laws (conserved densities) of a model of a nonlinear Scrodinger equation with PT-symmetric potentials and inhomogeneity.

Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of…

We prove the precise inversion of adjunction formula for quotient singularities. As an application, we prove the semi-continuity of minimal log discrepancies for hyperquotient singularities. This paper is a continuation of arXiv:2011.07300,…

A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…

This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following the work of Bouchut and James (Comm. Partial Diff. Eq., 24, 1999), a notion of duality solution for…

A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…

We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…

For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.

Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…

Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…

Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a…

The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u) u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which…