Related papers: A new class of linearizable equations
We consider a specific type of nonlinear partial differential equations (PDE) that appear in mathematical finance as the result of solving some optimization problems. We review some existing in the literature examples of such problems, and…
Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a…
A family of solutions of the Jacobi PDEs is investigated. This family is $n$-dimensional, of arbitrary nonlinearity and can be globally analyzed (thus improving the usual local scope of Darboux theorem). As an outcome of this analysis it is…
We examine whether the Painleve property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of…
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…
An algorithmic method using conservation law multipliers is introduced that yields necessary and sufficient conditions to find invertible mappings of a given nonlinear PDE to some linear PDE and to construct such a mapping when it exists.…
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…
Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…
In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable algebras of…
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
We discuss Lie algebras of the Lie symmetry groups of two generically non-integrable equations in one temporal and two space dimensions arising in different contexts. The first is a generalization of the KP equation and contains 9 arbitrary…
Selection of 25 examples from extensive nontrivial families for different types of nonlinear PDEs and their formal general solutions are given. The main goal here is to show on examples the types of solvable PDEs and what their general…
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in…
An explicit formula to find symmetry recursion operators for partial differential equations (PDEs) is obtained from new results connecting variational integrating factors and non-variational symmetries. The formula is special case of a…
The branching methods developed are effective methods to solve some semi linear PDEs and are shown numerically to be able to solve some full non linear PDEs. These methods are however restricted to some small coefficients in the PDE and…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability…
The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive…