Order reduction for critical traveling wave problems

Homoclinic Solutions for Fourth Order Traveling Wave Equations

We consider homoclinic solutions of fourth order equations u ′′′′ + βu ′′ + Vu(u) = 0 in R , where V (u) is either the suspension bridge type V (u) = eu − 1 − u or SwiftHohenberg type V (u) = 1 4 (u2 − 1)2. For the suspension bridge type equation, we prove existence of a homoclinic solution for all β ∈ (0, β∗) where β∗ = 0.7427 · · · . For the Swift-Hohenberg type equation, we prove existence o...

Traveling Wave Solutions of Fourth Order PDEs for Image Processing

Second Harmonic Reduction of Traveling Wave Tube Amplifier Using Ferrite Material

Traveling Wave Tubes (TWTs) consist of different elements. The most important element of TWT is the RF circuit. RF circuits in helix TWTs need a dielectric support to hold the helix; this support also has an effect in electromagnetic properties of RF circuits. A novel dielectric support is proposed to reduce the second harmonic of helix TWTs. The dielectric support in this structure consists of...

Model Order Reduction for Coupled Problems

In this survey, we provide an overview of model order reduction (MOR) methods applied to coupled systems. The coupling can be linear or nonlinear, weak or strong. Physically, the coupling may come from structurestructure coupling, fluid-structure or fluid-fluid interaction, electro-thermal coupling, electroor thermal-mechanical coupling, or circuit-device coupling. Different MOR methods for cou...

Some traveling wave solutions of soliton family

Solitons are ubiquitous and exist in almost every area from sky to bottom. For solitons to appear, the relevant equation of motion must be nonlinear. In the present study, we deal with the Korteweg-deVries (KdV), Modied Korteweg-de Vries (mKdV) and Regularised LongWave (RLW) equations using Homotopy Perturbation method (HPM). The algorithm makes use of the HPM to determine the initial expansion...