Evaluation of Traveling Wave Models for Carangiform Swimming Based on Complex Modes

2018 ◽  
pp. 335-341
Author(s):  
Mahdieh Tanha ◽  
Brian F. Feeny
Keyword(s):  
Traveling Wave ◽  
Complex Modes ◽  
Wave Models ◽  
Carangiform Swimming

Completing the Study of Traveling Wave Solutions for Three Two-Component Shallow Water Wave Models

2020 ◽  
Vol 30 (03) ◽  
pp. 2050036 ◽  
Author(s):  
Jibin Li ◽  
Guanrong Chen ◽  
Jie Song
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Two Component ◽  
Wave Models

For three two-component shallow water wave models, from the approach of dynamical systems and the singular traveling wave theory developed in [Li & Chen, 2007], under different parameter conditions, all possible bounded solutions (solitary wave solutions, pseudo-peakons, periodic peakons, as well as smooth periodic wave solutions) are derived. More than 19 explicit exact parametric representations are obtained. Of more interest is that, for the integrable two-component generalization of the Camassa–Holm equation, it is found that its [Formula: see text]-traveling wave system has a family of pseudo-peakon wave solutions. In addition, its [Formula: see text]-traveling wave system has two families of uncountably infinitely many solitary wave solutions. The new results complete a recent study by Dutykh and Ionescu-Kruse [2016].

scholarly journals External cavity modes in Lang-Kobayashi and traveling wave models

2006 ◽  
Author(s):  
Mindaugas Radziunas ◽  
Hans-Jürgen Wünsche ◽  
Bernd Krauskopf ◽  
Matthias Wolfrum
Keyword(s):  
Traveling Wave ◽  
External Cavity ◽  
Cavity Modes ◽  
Wave Models

EXTENDED TANH-METHODS AND SOLITONIC SOLUTIONS OF THE GENERAL SHALLOW WATER WAVE MODELS

2004 ◽  
Vol 15 (03) ◽  
pp. 363-370 ◽  
Author(s):  
WOO-PYO HONG ◽  
SEOUNG-HWAN PARK
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Traveling Wave ◽  
Water Wave ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Shallow Water Wave ◽  
Wave Solutions ◽  
Wave Models

Based on the two recent extended tanh-function methods, we find traveling-wave solutions for the general shallow water wave models. The obtained solutions include periodical, singular and solitary-wave solutions.

scholarly journals Population genetics of polymorphism and divergence in rapidly evolving populations

2021 ◽  
Author(s):  
Matthew J. Melissa ◽  
Benjamin H Good ◽  
Daniel S Fisher ◽  
Michael M. Desai
Keyword(s):  
Traveling Wave ◽  
Population Genetic ◽  
Evolutionary Dynamics ◽  
Frequency Spectra ◽  
Fitness Effects ◽  
Wide Range ◽  
Fixation Probabilities ◽  
Wave Models ◽  
Traditional Population ◽  
Evolving Populations

In rapidly evolving populations, numerous beneficial and deleterious mutations can arise and segregate within a population at the same time. In this regime, evolutionary dynamics cannot be analyzed using traditional population genetic approaches that assume that sites evolve independently. Instead, the dynamics of many loci must be analyzed simultaneously. Recent work has made progress by first analyzing the fitness variation within a population, and then studying how individual lineages interact with this traveling fitness wave. However, these "traveling wave" models have previously been restricted to extreme cases where selection on individual mutations is either much faster or much slower than the typical coalescent timescale T_c. In this work, we show how the traveling wave framework can be extended to intermediate regimes in which the scaled fitness effects of mutations (T_c s) are neither large nor small compared to one. This enables us to describe the dynamics of populations subject to a wide range of fitness effects, and in particular, in cases where it is not immediately clear which mutations are most important in shaping the dynamics and statistics of genetic diversity. We use this approach to derive new expressions for the fixation probabilities and site frequency spectra of mutations as a function of their scaled fitness effects, along with related results for the coalescent timescale T_c and the rate of adaptation or Muller's ratchet. We find that competition between linked mutations can have a dramatic impact on the proportions of neutral and selected polymorphisms, which is not simply summarized by the scaled selection coefficient T_c s. We conclude by discussing the implications of these results for population genetic inferences.

scholarly journals On the stability of traveling wave solutions to thin-film and long-wave models for film flows inside a tube

2021 ◽  
Vol 415 ◽  
pp. 132750 ◽  
Author(s):  
Roberto Camassa ◽  
Jeremy L. Marzuola ◽  
H. Reed Ogrosky ◽  
Sterling Swygert
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Wave Models ◽  
The Stability ◽  
Film Flows

Bifurcations and Exact Traveling Wave Solutions in Two Nonlinear Wave Systems

2021 ◽  
Vol 31 (06) ◽  
pp. 2150093
Author(s):  
Yan Zhou ◽  
Jinsen Zhuang ◽  
Jibin Li
Keyword(s):  
Nonlinear Wave ◽  
Traveling Wave ◽  
Systems Approach ◽  
Traveling Wave Solutions ◽  
Wave Theory ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave ◽  
Wave Models

This paper studies two nonlinear wave models. From the dynamical systems approach and using the singular traveling wave theory developed by [Li & Chen, 2007], all possible bounded solutions (solitary wave solutions, periodic wave solutions, as well as kink and anti-kink wave solutions) are obtained under different parameter conditions. More than 27 explicit exact parametric representations are derived. The new results complete the recent studies of [Rogers et al., 2020; Zayeda et al., 2020].

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