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Convergence of solitarywave solutions in a perturbed biHamiltonian dynamical system I. Compactions and peakons
1.  School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States, United States 
[1] 
Y. A. Li, P. J. Olver. Convergence of solitarywave solutions in a perturbed bihamiltonian dynamical system ii. complex analytic behavior and convergence to nonanalytic solutions. Discrete and Continuous Dynamical Systems, 1998, 4 (1) : 159191. doi: 10.3934/dcds.1998.4.159 
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Jerry L. Bona, Angel Durán, Dimitrios Mitsotakis. Solitarywave solutions of BenjaminOno and other systems for internal waves. I. approximations. Discrete and Continuous Dynamical Systems, 2021, 41 (1) : 87111. doi: 10.3934/dcds.2020215 
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Mathias Nikolai Arnesen. Existence of solitarywave solutions to nonlocal equations. Discrete and Continuous Dynamical Systems, 2016, 36 (7) : 34833510. doi: 10.3934/dcds.2016.36.3483 
[4] 
Jerry L. Bona, Didier Pilod. Stability of solitarywave solutions to the HirotaSatsuma equation. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 13911413. doi: 10.3934/dcds.2010.27.1391 
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Min Chen, Nghiem V. Nguyen, ShuMing Sun. Solitarywave solutions to Boussinesq systems with large surface tension. Discrete and Continuous Dynamical Systems, 2010, 26 (4) : 11531184. doi: 10.3934/dcds.2010.26.1153 
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Tong Yang, Seiji Ukai, Huijiang Zhao. Stationary solutions to the exterior problems for the Boltzmann equation, I. Existence. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 495520. doi: 10.3934/dcds.2009.23.495 
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Stephen Anco, Daniel Kraus. Hamiltonian structure of peakons as weak solutions for the modified CamassaHolm equation. Discrete and Continuous Dynamical Systems, 2018, 38 (9) : 44494465. doi: 10.3934/dcds.2018194 
[8] 
David Cheban. I. U. Bronshtein's conjecture for monotone nonautonomous dynamical systems. Discrete and Continuous Dynamical Systems  B, 2019, 24 (3) : 10951113. doi: 10.3934/dcdsb.2019008 
[9] 
Stephen C. Anco, Elena Recio. Accelerating dynamical peakons and their behaviour. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 61316148. doi: 10.3934/dcds.2019267 
[10] 
Paweł Lubowiecki, Henryk Żołądek. The HessAppelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443467. doi: 10.3934/jgm.2012.4.443 
[11] 
Ugur G. Abdulla. On the optimal control of the free boundary problems for the second order parabolic equations. I. Wellposedness and convergence of the method of lines. Inverse Problems and Imaging, 2013, 7 (2) : 307340. doi: 10.3934/ipi.2013.7.307 
[12] 
Feimin Huang, Yi Wang, Tong Yang. Fluid dynamic limit to the Riemann Solutions of Euler equations: I. Superposition of rarefaction waves and contact discontinuity. Kinetic and Related Models, 2010, 3 (4) : 685728. doi: 10.3934/krm.2010.3.685 
[13] 
Anna Capietto, Walter Dambrosio, Tiantian Ma, Zaihong Wang. Unbounded solutions and periodic solutions of perturbed isochronous Hamiltonian systems at resonance. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 18351856. doi: 10.3934/dcds.2013.33.1835 
[14] 
Zhensu Wen, Guanrong Chen. Solitary waves, periodic peakons and compactons on foliations in a Hertz chain model. Discrete and Continuous Dynamical Systems  S, 2022 doi: 10.3934/dcdss.2022072 
[15] 
V. Barbu. Periodic solutions to unbounded Hamiltonian system. Discrete and Continuous Dynamical Systems, 1995, 1 (2) : 277283. doi: 10.3934/dcds.1995.1.277 
[16] 
Jibin Li, Yi Zhang. Exact solitary wave and quasiperiodic wave solutions for four fifthorder nonlinear wave equations. Discrete and Continuous Dynamical Systems  B, 2010, 13 (3) : 623631. doi: 10.3934/dcdsb.2010.13.623 
[17] 
Kai Yan. On the blow up solutions to a twocomponent cubic CamassaHolm system with peakons. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 45654576. doi: 10.3934/dcds.2020191 
[18] 
Jibin Li. Family of nonlinear wave equations which yield loop solutions and solitary wave solutions. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 897907. doi: 10.3934/dcds.2009.24.897 
[19] 
Oleg Makarenkov, Paolo Nistri. On the rate of convergence of periodic solutions in perturbed autonomous systems as the perturbation vanishes. Communications on Pure and Applied Analysis, 2008, 7 (1) : 4961. doi: 10.3934/cpaa.2008.7.49 
[20] 
Jibin Li, Yi Zhang. On the traveling wave solutions for a nonlinear diffusionconvection equation: Dynamical system approach. Discrete and Continuous Dynamical Systems  B, 2010, 14 (3) : 11191138. doi: 10.3934/dcdsb.2010.14.1119 
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