American Institute of Mathematical Sciences

Advanced
January  1998, 4(1): 159-191. doi: 10.3934/dcds.1998.4.159

Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions

Y. A. Li 1, and  P. J. Olver 1,

1. 

School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States

Received  December 1996 Revised  January 1997 Published  October 1997

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except for at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support.
Keywords: Solitary-wave solutions, bi-Hamiltonian dynamical system, complex analytic behavior..
Mathematics Subject Classification: 34A20, 34C35, 35B65, 58F05, 76B2.
Citation: Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-hamiltonian dynamical system ii. complex analytic behavior and convergence to non-analytic solutions. Discrete & Continuous Dynamical Systems - A, 1998, 4 (1) : 159-191. doi: 10.3934/dcds.1998.4.159
[1]

Y. A. Li, P. J. Olver. Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system I. Compactions and peakons. Discrete & Continuous Dynamical Systems - A, 1997, 3 (3) : 419-432. doi: 10.3934/dcds.1997.3.419
[2]

Mathias Nikolai Arnesen. Existence of solitary-wave solutions to nonlocal equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3483-3510. doi: 10.3934/dcds.2016.36.3483
[3]

Jerry L. Bona, Didier Pilod. Stability of solitary-wave solutions to the Hirota-Satsuma equation. Discrete & Continuous Dynamical Systems - A, 2010, 27 (4) : 1391-1413. doi: 10.3934/dcds.2010.27.1391
[4]

Min Chen, Nghiem V. Nguyen, Shu-Ming Sun. Solitary-wave solutions to Boussinesq systems with large surface tension. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1153-1184. doi: 10.3934/dcds.2010.26.1153
[5]

Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I. approximations. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020215
[6]

Jianfeng Feng, Mariya Shcherbina, Brunello Tirozzi. Dynamical behaviour of a large complex system. Communications on Pure & Applied Analysis, 2008, 7 (2) : 249-265. doi: 10.3934/cpaa.2008.7.249
[7]

Jibin Li, Fengjuan Chen. Exact travelling wave solutions and their dynamical behavior for a class coupled nonlinear wave equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 163-172. doi: 10.3934/dcdsb.2013.18.163
[8]

V. Barbu. Periodic solutions to unbounded Hamiltonian system. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 277-283. doi: 10.3934/dcds.1995.1.277
[9]

Jibin Li, Yi Zhang. Exact solitary wave and quasi-periodic wave solutions for four fifth-order nonlinear wave equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 623-631. doi: 10.3934/dcdsb.2010.13.623
[10]

Jibin Li. Family of nonlinear wave equations which yield loop solutions and solitary wave solutions. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 897-907. doi: 10.3934/dcds.2009.24.897
[11]

Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusion-convection equation: Dynamical system approach. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 1119-1138. doi: 10.3934/dcdsb.2010.14.1119
[12]

Kuijie Li, Tohru Ozawa, Baoxiang Wang. Dynamical behavior for the solutions of the Navier-Stokes equation. Communications on Pure & Applied Analysis, 2018, 17 (4) : 1511-1560. doi: 10.3934/cpaa.2018073
[13]

Guanggan Chen, Jian Zhang. Asymptotic behavior for a stochastic wave equation with dynamical boundary conditions. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1441-1453. doi: 10.3934/dcdsb.2012.17.1441
[14]

Sen-Zhong Huang, Peter Takáč. Global smooth solutions of the complex Ginzburg-Landau equation and their dynamical properties. Discrete & Continuous Dynamical Systems - A, 1999, 5 (4) : 825-848. doi: 10.3934/dcds.1999.5.825
[15]

N. I. Karachalios, H. E. Nistazakis, A. N. Yannacopoulos. Remarks on the asymptotic behavior of solutions of complex discrete Ginzburg-Landau equations. Conference Publications, 2005, 2005 (Special) : 476-486. doi: 10.3934/proc.2005.2005.476
[16]

Jian Zhang, Wen Zhang, Xiaoliang Xie. Existence and concentration of semiclassical solutions for Hamiltonian elliptic system. Communications on Pure & Applied Analysis, 2016, 15 (2) : 599-622. doi: 10.3934/cpaa.2016.15.599
[17]

José Raúl Quintero, Juan Carlos Muñoz Grajales. Solitary waves for an internal wave model. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5721-5741. doi: 10.3934/dcds.2016051
[18]

Xiaowan Li, Zengji Du, Shuguan Ji. Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation. Communications on Pure & Applied Analysis, 2019, 18 (6) : 2961-2981. doi: 10.3934/cpaa.2019132
[19]

Rui Liu. Several new types of solitary wave solutions for the generalized Camassa-Holm-Degasperis-Procesi equation. Communications on Pure & Applied Analysis, 2010, 9 (1) : 77-90. doi: 10.3934/cpaa.2010.9.77
[20]

C. M. Evans, G. L. Findley. Analytic solutions to a class of two-dimensional Lotka-Volterra dynamical systems. Conference Publications, 2001, 2001 (Special) : 137-142. doi: 10.3934/proc.2001.2001.137

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (30)
  • HTML views (0)
  • Cited by (39)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences