We have presented a new hyperbolic auxiliary function method for obtaining traveling wave solutions of nonlinear partial differential equations. Applying this, exact traveling wave solutions for the coupled Sine-Gordon equations are constructed.

Introduction At high magnetic field strengths, travelling wave MRI can be used to solve the standing wave problem of volume resonators [1]. However, travelling wave MRI suffers from electromagnetic field-attenuation and high whole body energy deposition (SAR), so that only the distal parts of the body can be imaged. In this work we introduce a new travelling wave RF coil. The coil guides the tr...

The theory, design and experimental results of a wideband 140 GHz, 1 kW pulsed gyro-traveling wave amplifier are presented. The gyro-TWA operates in the HE(0,6) mode of an overmoded quasi-optical waveguide using a gyrating electron beam. The electromagnetic theory, interaction theory, design processes and experimental procedures are described in detail. At 37.7 kV and 2.7 A beam current, the ex...

Electrostatic traveling wave (ETW) methods have shown promising performance in dust mitigation of solar panels, particle transport and separation situ space resource utilization, cell manipulation, biology. The ETW field distribution is required to analyze the forces applied particles evaluate design parameters. This study presents numerical results generated by a parallel electrode array using...

Traveling wave solutions of reaction-diffusion equations are well studied for Lipschitz continuous monostable and bistable reaction functions. These special play a key role in mathematical biology particular the study ecological invasions. However, if there more than two stable steady states, invasion phenomenon may become intricate involve intermediate steps, which leads one to consider not si...

The mechanism for passive cochlear tuning remains unsettled. Early models considered the organ of Corti complex (OCC) as a succession of spring-mass resonators. Later, traveling wave models showed that passive tuning could arise through the interaction of cochlear fluid mass and OCC stiffness without local resonators. However, including enough OCC mass to produce local resonance enhanced the tu...

We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-...

In this article, we apply the Multiquadric radial basis function (RBF) interpo-lation method for nding the numerical approximation of traveling wave solu-tions of the Kawahara equation. The scheme is based on the Crank-Nicolsonformulation for space derivative. The performance of the method is shown innumerical examples.