scholarly journals Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system

2017 ◽  
Vol 347 ◽  
pp. 21-41 ◽  
Author(s):  
Rhys Bury ◽  
Alexander V. Mikhailov ◽  
Jing Ping Wang
Keyword(s):  
Two Dimensional ◽  
Volterra System ◽  
Wave Fronts ◽  
Soliton Interactions

Complete integrability and complex solitons for generalized Volterra system with branched dispersion

2020 ◽  
Vol 34 (29) ◽  
pp. 2050274 ◽  
Author(s):  
Corina N. Babalic
Keyword(s):  
Dispersion Relation ◽  
Asymptotic Analysis ◽  
Complete Integrability ◽  
Graphical Representations ◽  
Two Dimensional ◽  
Volterra System ◽  
Bilinear Formalism ◽  
Hirota Bilinear ◽  
Multisoliton Solutions ◽  
Periodic Reduction

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

scholarly journals Data-driven modeling of two-dimensional detonation wave fronts

Wave Motion ◽  
2022 ◽  
pp. 102879
Author(s):  
Ariana Mendible ◽  
Weston Lowrie ◽  
Steven L. Brunton ◽  
J. Nathan Kutz
Keyword(s):  
Detonation Wave ◽  
Data Driven ◽  
Two Dimensional ◽  
Wave Fronts ◽  
Data Driven Modeling

The KP theory and Mach reflection

2016 ◽  
Vol 800 ◽  
pp. 766-786 ◽  
Author(s):  
Yuji Kodama ◽  
Harry Yeh
Keyword(s):  
Normal Form ◽  
Shallow Water ◽  
Mach Reflection ◽  
Two Dimensional ◽  
Kp Equation ◽  
Normal Form Theory ◽  
Soliton Interactions ◽  
Form Theory ◽  
Water Field ◽  
Kp Theory

Interactions of two line solitons in the two-dimensional shallow-water field are studied based on the Kadomtsev–Petviashvili (KP) theory. With the use of the normal form, the extended KP equation with higher-order correction is derived. This extended KP theory improves significantly the predictability of the original KP theory for soliton interactions with finite oblique angles. The previously existing discrepancy between the experiments and the theory in the Mach reflection problem is now resolved by the normal form theory.

Real‐time visualization of acoustic wave fronts by using a two‐dimensional microphone array

1988 ◽  
Vol 84 (4) ◽  
pp. 1373-1377 ◽  
Author(s):  
Yukio Hiranaka ◽  
Osamu Nishii ◽  
Takayuki Genma ◽  
Hiro Yamasaki
Keyword(s):  
Acoustic Wave ◽  
Real Time ◽  
Microphone Array ◽  
Two Dimensional ◽  
Wave Fronts ◽  
Real Time Visualization

Triangular Cellular Automata for Computing Two-Dimensional Elastodynamic Response on Arbitrary Domains

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Ryan K. Hopman ◽  
Michael J. Leamy
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Cellular Automata ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Two Dimensional ◽  
Wave Fronts ◽  
Rule Set ◽  
Spurious Oscillations ◽  
Elastodynamic Response

This study extends a recently developed cellular automata (CA) modeling approach (Leamy, 2008, “Application of Cellular Automata Modeling to Seismic Elastodynamics,” Int. J. Solids Struct., 45(17), pp. 4835–4849) to arbitrary two-dimensional geometries via the development of a rule set governing triangular automata (cells). As in the previous rectangular CA method, each cell represents a state machine, which updates in a stepped manner using a local “bottom-up” rule set and state input from neighboring cells. Notably, the approach avoids the need to develop and solve partial differential equations and the complexity therein. The elastodynamic responses of several general geometries and loading cases (interior, Neumann, and Dirichlet) are computed with the method and then compared with results generated using the earlier rectangular CA and finite element approaches. Favorable results are reported in all cases with numerical experiments indicating that the extended CA method avoids, importantly, spurious oscillations at the front of sharp wave fronts.

Interpretation of three-soliton interactions in terms of resonant triads

1978 ◽  
Vol 87 (1) ◽  
pp. 17-31 ◽  
Author(s):  
D. Anker ◽  
N. C. Freeman
Keyword(s):  
Soliton Solution ◽  
Analytic Solution ◽  
Vries Equation ◽  
Two Dimensional ◽  
Soliton Interactions ◽  
Resonant Interactions ◽  
De Vries ◽  
Computer Calculations ◽  
Resonant Triads

The three-soliton solution of the two-dimensional Korteweg-de Vries equation is analysed to show that the structure of the interaction can be represented in terms of the motion of two-soliton resonant interactions (resonant triads) as described by Miles (1977). The schematic development of the interaction with time is obtained and shown to approximate closely to computer calculations of the analytic solution. Similar results follow for interactions of more solitons and other equations.

scholarly journals Some New Results on the Lotka-Volterra System with Variable Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yangzi Hu ◽  
Fuke Wu ◽  
Chengming Huang
Keyword(s):  
Volterra Model ◽  
Time Varying ◽  
Two Dimensional ◽  
Variable Delay ◽  
Volterra System ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Varying Delay

This paper discusses the stochastic Lotka-Volterra system with time-varying delay. The nonexplosion, the boundedness, and the polynomial pathwise growth of the solution are determined once and for all by the same criterion. Moreover, this criterion is constructed by the parameters of the system itself, without any uncertain one. A two-dimensional stochastic delay Lotka-Volterra model is taken as an example to illustrate the effectiveness of our result.

Sign in / Sign up

Export Citation Format

Share Document