scholarly journals Global Conservative and Multipeakon Conservative Solutions for the Modified Camassa-Holm System with Coupling Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Huabin Wen ◽  
Yujuan Wang ◽  
Yongduan Song ◽  
Hamid Reza Karimi
Keyword(s):  
Wave Breaking ◽  
Mutual Coupling ◽  
Coupling Effect ◽  
Original System ◽  
Equivalent System ◽  
Coupling Effects ◽  
Two Component

This paper investigates the continuation of solutions to the modified coupled two-component Camassa-Holm system after wave breaking. The underlying problem is rather challenging due to the mutual coupling effect between two components in the system. By introducing a novel transformation that makes use of a skillfully defined characteristic and a set of newly defined variables, the original system is converted into a Lagrangian equivalent system, from which the global conservative solution is obtained, which further allows for the establishment of the multipeakon conservative solution of the system. The results obtained herein are deemed useful for understanding the inevitable phenomenon near wave breaking.

scholarly journals Modified Minkowski Fractal Unit Cell for Reflectarrays with Low Sensitivity to Mutual Coupling Effects

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Sandra Costanzo ◽  
Francesca Venneri ◽  
Giuseppe Di Massa
Keyword(s):  
Mutual Coupling ◽  
Coupling Effect ◽  
Single Layer ◽  
Unit Cell ◽  
Phase Curve ◽  
Lower Sensitivity ◽  
Coupling Effects ◽  
Infinite Array ◽  
Low Sensitivity ◽  
Phase Design

A single-layer miniaturized reflectarray element with low sensitivity to mutual coupling effects of surrounding elements is presented in this paper. The configuration is proposed to preserve the effectiveness of the infinite array approach in those applications requiring reflectarrays with very small interelement spacing. The inherent ability of the proposed geometry to be adopted in highly miniaturized cells is demonstrated through an extensive analysis of mutual coupling effects on reflectarray phase design curves. In order to prove the independence of the proposed cell to mutual coupling effect, the phase curve variations due to the presence of different surrounding elements with respect to the case of identical cells are evaluated using the well-known extended local periodicity method. Small and negligible mutual coupling errors are retrieved for the proposed miniaturized unit cell, thus demonstrating lower sensitivity to mutual coupling adverse effects.

scholarly journals On the Global Dissipative and Multipeakon Dissipative Behavior of the Two-Component Camassa-Holm System

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Yujuan Wang ◽  
Yongduan Song ◽  
Hamid Reza Karimi
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water System ◽  
Original System ◽  
Collision Time ◽  
Two Component ◽  
Shallow Water System

The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global dissipative solution, which constructs a semigroup, and the multipeakon dissipative solution.

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

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