We consider the damped/driven (modified) cubic NLS equation on a large torus with properly scaled forcing and dissipation, decompose its solutions to formal series in amplitude. study second order truncation of this prove that when amplitude goes zero torus’ size infinity energy spectrum truncated becomes close solution wave kinetic equation. Next we discuss higher truncations series.

In this paper, we give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation ẅ + ηẇ + γAw = u(t) + f(t, w, u(t)), on a Hilbert space. The distributed control u ∈ L2 and the operator A is positive definite self-adjoint unbounded with compact resolvent. The nonlinear term f is a continuous function on t and globally Lipschitz in the other variabl...

Abstract The aim of the paper is to study problem $$\begin{aligned} {\left\{ \begin{array}{ll} u_{tt}+du_t-c^2\Delta u=0 \qquad &{}\text {in}\, {\mathbb {R}}\times \Omega ,\\ \mu v_{tt}- \textrm{div}_\Gamma (\sigma \nabla _\Gamma v)+\delta v_t+\kappa v+\rho u_t =0\qquad {on}\, \Gamma _1,\\ v_t =\partial _\nu u\qquad \partial _0,\\ u(0,x)=u_0(x),\quad u_t(0,x)=u_1(x) &{} \text v(0,x)=v_0...

This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model propagation weakly dispersive waves in a fluid. With help Cole—Hopf transform, Hirota bilinear equation established, then symbolic computation with ansatz function schemes employed search for diverse exact solutions. Some new results such as...