Related papers: Right and Wrong Ans\"atze for Nonlinear Waves in S…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
The Fisher-KPP equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms is considered. The existence of oscillatory travelling wave solutions is proved for this model. Conditions for the existence of such…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We formulate the stochastic differential equations for non-linear hydrodynamic fluctuations. The equations incorporate the random forces through a random stress tensor and random heat flux as in the Landau and Lifshitz theory. However, the…
We study propagation of stationary waves in disordered non-linear media described by the non-linear Schroedinger equation and show that for given boundary conditions and a given coherent wave incident on a sample the number of solutions of…
The traveling wave solutions to some nonlinear conformable time fractional partial differential equations in RLW-class are set up by using sech and csch ansatzs. The conformable time fractional forms of the equal-width (EW), regularized…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models,…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard…
We study the traveling wave solutions to a reaction diffusion system modeling the public goods game with altruistic behaviors. The existence of the waves is derived through monotone iteration of a pair of classical upper- and lower…
The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…
Proposed in this paper is a numerical procedure to generate periodic traveling wave solutions of some nonlinear dispersive wave equations. The method is based on a suitable modification of a fixed point algorithm of Petviahvili type and…
The approach allowing is considered to represent the solutions such as stationary lonely waves of various nonlinear wave the equations as system of the ordinary differential equations in variable action - angle.
The existence of nonzero periodic travelling wave solutions for a general discrete nonlinear Schr\"odinger equation (DNLS) on finite one-dimensional lattices is proved. The DNLS features a general nonlinear term and variable range of…
We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. We derive convergence with an implicit rate…
Spatially periodic reaction-diffusion equations typically admit pulsating waves which describe the transition from one steady state to another. Due to the heterogeneity, in general such an equation is not invariant by rotation and therefore…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…