A novel generalized dispersion equation to design circumferential wave fluid sensors

Optimal design of sensors for a damped wave equation

In this paper we model and solve the problem of shaping and placing in an optimal way sensors for a wave equation with constant damping in a bounded open connected subset Ω of IRn. Sensors are modeled by subdomains of Ω of a given measure L|Ω|, with 0 < L < 1. We prove that, if L is close enough to 1, then the optimal design problem has a unique solution, which is characterized by a finite numb...

New study to construct new solitary wave solutions for generalized sinh- Gordon equation

In this work, we successfully construct the new exact traveling wave solutions of the generalized Sinh–Gordon equation by new application of the homogeneous balance method. The idea introduced in this paper can be applied to other nonlinear evolution equations.

Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation

We consider a generalized hyperelastic-rod wave equation (or generalized Camassa– Holm equation) describing nonlinear dispersive waves in compressible hyperelastic rods. We establish existence of a strongly continuous semigroup of global weak solutions for any initial data from H1(R). We also present a “weak equals strong”uniqueness result.

A Novel Generalized Nonlinear Dispersion Equation for Five-Layer Waveguides with Kerr-like Nonlinearity

Traveling Wave Solutions of the Generalized b-family Equation with Dispersion

This paper introduces a family of evolutionary 1+1 PDEs that describe the balance between convection and stretching in the dynamics of 1D nonlinear waves in fluids. It is reversible in time and parity invariant. In the paper, special solutions are discussed for b = 0 and for b ∕= 0, the general solutions are given.When b = 3 and b = −1 , the paper obtains the exact solutions of the generalized ...