Heteroclinic solutions for the extended Fisher–Kolmogorov equation

Various Heteroclinic Solutions for the Coupled Schrödinger-Boussinesq Equation

and Applied Analysis 3

Multitransition Homoclinic and Heteroclinic Solutions of the Extended Fisher-kolmogorov Equation

Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation

We study the differential equation ẍ(t) = a(t)V ′(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) → l > 0 as |t| → ∞. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t)→ −1 as t→ −∞ and x(t) → 1 as t → ∞. The assumptions allow l − a(t) to change sign for arbitrarily large values of |...

Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation

This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being f...

Analytical solutions for the fractional Fisher's equation

In this paper, we consider the inhomogeneous time-fractional nonlinear Fisher equation with three known boundary conditions. We first apply a modified Homotopy perturbation method for translating the proposed problem to a set of linear problems. Then we use the separation variables  method to solve obtained problems. In examples, we illustrate that by right choice of source term in the modified...