Related papers: An explicit Maclaurin series solution to a classic…

A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…

Classes of third order non-Abelian evolution equations linked to that of Korteweg-de Vries-type are investigated and their connections represented in a non-commutative B\"acklund chart, generalizing results in [Fuchssteiner B., Carillo S.,…

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…

The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…

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…

This paper is concerned with a scalar nonlinear convolution equation which appears naturally in the theory of traveling waves for monostable evolution models. First, we prove that each bounded positive solution of the convolution equation…

In this work, we propose and analyze a residual-minimization strategy for the numerical solution of nonlinear PDEs posed in Banach spaces. Given a finite-dimensional trial space and a suitably enriched discrete test space (of higher…

We derive a closed-form expression for the Green function of linear evolution equations with the Dirichlet boundary condition for an arbitrary region, based on the singular perturbation approach to boundary problems.

The original Miura transformation, considered as a nonlinear potential transformation, is applicable to a continual class of evolution equations, not only to discrete integrable equations and their hierarchies. The same continual class of…

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a…

Consider the nonautonomous semilinear evolution equation of type: $(\star) \; u'(t)=A(t)u(t)+f(t,u(t)), \; t \in \mathbb{R},$ where $ A(t), \ t\in \mathbb{R} $ is a family of closed linear operators in a Banach space $X$, the nonlinear term…

Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…

Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the…

In this work we present a solution of the Boussinesq equation. The derived formulas include solitons, Schwartz class solutions and solutions, possessing singularities on a closed set Z of the (x,t) domain, obtained from the zeros of the tau…

In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its…

We consider the functional Schrodinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrodinger equation whose…

We establish new global bifurcation theorems for dynamical systems in terms of local semiflows on complete metric spaces. These theorems are applied to the nonlinear evolution equation $u_t+A u=f_\lambda(u)$ in a Banach space $X$, where $A$…

The non-commutative strategy developed by Bagarello (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis of systems of ordinary differential equations (ODEs) is extended to a class of partial…

We show that, under certain smoothness conditions, a Brownian martingale, when evaluated at a fixed time, can be represented via an exponential formula at a later time. The time-dependent generator of this exponential operator only depends…

This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in $D$-dimensional spacetime. These solutions are found by…