S itting in the enveloping quietness of an anechoic chamber, or other quiet spot, you soon become aware that the ear makes its own distinctive sounds. Whistling, buzzing, hissing, perhaps a chiming chorus of many tones—such continuous sounds seem remarkably nonbiological to my perception, more in the realm of the electronic. Even more remarkable, put a sensitive microphone in the ear canal and ...

In this paper, by using bifurcation method, we successfully find the K(2, 2) equation with osmosis dispersion ut+(u )x− (u)xxx = 0 possess two new types of travelling wave solutions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained....

The gyrotron travelling wave tube (gyro-TWT) is an ideal high-power, broadband vacuum electron amplifier in millimeter and sub-millimeter bands. It can be applied as the source of imaging radar to improve resolution operating range. To satisfy requirements W-band high-resolution radar, design experimentation TE02 mode gyro-TWT were carried out. In this paper, designs key components are introduc...

Periodic travelling waves (wavetrains) are an important solution type for many partial differential equations. In this paper I review the use of numerical continuation for studying these solutions. I discuss the calculation of the form and stability of a given periodic travelling wave, and the calculation of boundaries in a two-dimensional parameter plane for wave existence and stability. I als...

We use a numerical method that was described in Part 1 (Marcus 1984a) to solve the time-dependent Navier-Stokes equation and boundary conditions that govern Taylor-Couette flow. We compute several stable axisymmetric Taylor-vortex equilibria and several stable non-axisymmetric wavy-vortex flows that correspond to one travelling wave. For each flow we compute the energy, angular momentum, torque...

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...

The modified tanh-coth function method is used to obtain new exact travelling wave solutions for Zhiber-Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd-Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation. Exact travelling wave solutions for each equation are derived and expressed in terms of hyperbolic functions, trigonometric functions an...

Under the travelling wave transformation, Calogero-Degasperis-Focas equation was reduced to an ordinary differential equation. Using a symmetry group of one-parameter, this ODE was reduced to a second order linear inhomogeneous ODE. Furthermore, we applied the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classific...

In this paper, we explore more applications of the hyperbolic function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations (PDES), to special discrete nonlinear equations. Some exact travelling wave solution of the discrete sine-Gordon equation are obtained in terms of hyperbolic fun...

We consider a simplified model of vertical non-static groundwater flow, resulting in a Burgers’ diffusive equation extended with a third order term with mixed derivatives in space and time. This model is motivated by previous work on the existence of travelling wave solutions on a more general model. We investigate stability of travelling wave solutions of the simplified model, for which we fir...