scholarly journals Waves of maximal height for a class of nonlocal equations with inhomogeneous symbols

2021 ◽  
pp. 1-26
Author(s):  
Hung Le
Keyword(s):  
Traveling Wave ◽  
Convolution Operator ◽  
Wave Solution ◽  
Global Bifurcation ◽  
Traveling Wave Solution ◽  
Convolution Kernel ◽  
Bessel Potential ◽  
Nonlocal Equations ◽  
Maximal Height ◽  
Periodic Traveling Wave

In this paper, we consider a class of nonlocal equations where the convolution kernel is given by a Bessel potential symbol of order α for α > 1. Based on the properties of the convolution operator, we apply a global bifurcation technique to show the existence of a highest, even, 2 π-periodic traveling-wave solution. The regularity of this wave is proved to be exactly Lipschitz.

Periodic traveling-wave solution of the Sakuma-Nishiguchi equation

1996 ◽  
Vol 54 (19) ◽  
pp. 13484-13486 ◽  
Author(s):  
David R. Rowland ◽  
Zlatko Jovanoski
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

Periodic traveling wave solution for non-homogeneous BBM and KdVB equations

2017 ◽  
Vol 34 ◽  
pp. 563-573
Author(s):  
Marcos A. de Farias ◽  
Cezar I. Kondo ◽  
José R. dos Santos Filho
Keyword(s):  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solution ◽  
Periodic Traveling Wave

scholarly journals Nonlinear Stability of the Periodic Traveling Wave Solution for a Class of Coupled KdV Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cong Sun
Keyword(s):  
Nonlinear Stability ◽  
Implicit Function Theorem ◽  
Traveling Wave ◽  
Wave Solution ◽  
Function Method ◽  
Traveling Wave Solution ◽  
Implicit Function ◽  
Kdv Equations ◽  
Periodic Traveling Wave ◽  
Coupled Kdv Equations

In this paper, by applying the Jacobian ellipse function method, we obtain a group of periodic traveling wave solution of coupled KdV equations. Furthermore, by the implicit function theorem, the relation between some wave velocity and the solution’s period is researched. Lastly, we show that this type of solution is orbitally stable by periodic perturbations of the same wavelength as the underlying wave.

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

scholarly journals Stability Analysis of an Age-Structured SEIRS Model with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 455 ◽  
Author(s):  
Zhe Yin ◽  
Yongguang Yu ◽  
Zhenzhen Lu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Traveling Wave ◽  
Wave Solution ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Traveling Wave Solution ◽  
Age Structured ◽  
Nonlinear Autonomous System ◽  
Disease Free

This paper is concerned with the stability of an age-structured susceptible–exposed– infective–recovered–susceptible (SEIRS) model with time delay. Firstly, the traveling wave solution of system can be obtained by using the method of characteristic. The existence and uniqueness of the continuous traveling wave solution is investigated under some hypotheses. Moreover, the age-structured SEIRS system is reduced to the nonlinear autonomous system of delay ODE using some insignificant simplifications. It is studied that the dimensionless indexes for the existence of one disease-free equilibrium point and one endemic equilibrium point of the model. Furthermore, the local stability for the disease-free equilibrium point and the endemic equilibrium point of the infection-induced disease model is established. Finally, some numerical simulations were carried out to illustrate our theoretical results.

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