The Cauchy problem for the nonlinear one-dimensional sixth-order Boussinesq equation with logarithmic nonlinearity is concerned in this paper. Results of global existence and exponential growth solution are got framework potential well utilizing Galerkin method concavity at subcritical critical initial energy levels.

T his paper proposes a new unit root test against the alternative of symmetric or asymmetric exponential smooth transition autoregressive (AESTAR) nonlinearity that accounts for multiple smooth breaks. We provide small sample properties which indicate the test statistics have good empirical size and power. Also, we compared small sample properties of the test statistics with Christop...

We study the two dimensional non-linear Schrödinger equation with types of exponential non-linearities. It is well-known by a work Ruf–Sani (Ruf and Sani, 2013), that such models support solitary wave solutions, which are solutions some constrained minimization problem. show solitons spectrally unstable blow up.

Given a predesigned linear state feedback law for a linear plant ensuring (global) exponential stability of the linear closed loop, together with a certain level of performance, we address the problem of recovering (local or global) exponential stability and performance in the presence of plant input saturation and of a communication channel between the controller output and the saturated plant...

The self-accelerating beams such as the Airy beam show great potentials in many applications including optical manipulation, imaging and communication. However, their superior features during linear propagation could be easily corrupted by nonlinearity or spatial incoherence individually. Here we investigate how interaction of nonlinear affect quality beam, find that two destroying factors can ...

We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach w...