Decomposition of 2-Soliton Solutions for the Good Boussinesq Equations

References

• M.J. Ablowitz and H. Segur, Solitons and Inverse Scattering Transform, Philadelphia. SIAM, (1981).
   Google Scholar
• N. Benes, A. Kasman, and K. Young, On Decompositions of the KdV 2-Soliton, Journal of Nonlinear Science, 16 (2006) 179–200. doi: 10.1007/s00332-005-0709-2
   Web of Science ®Google Scholar
• M. Błaszak, On interacting solitons, Acta Phys. Pol., A74 (1988) 439.
   Google Scholar
• M. Błaszak, Soliton particles, Chapter 5 in Multi-Hamiltonian Theory of Dynamical Systems, (Springer Verlage, 1998).
   Google Scholar
• G. Bowtell and A.E. Stuart, A Particle Representation for Kortweg-de Vries Solitons, J. Math. Phys., 24 (1983) 969–981. doi: 10.1063/1.525786
   Web of Science ®Google Scholar
• Chun-Xia Li et al., Wronskian solutions of the Boussinesq equation-solitons, negatons, positons and complexitons, Inverse Problems, 23 (2007) 279. doi: 10.1088/0266-5611/23/1/015
   Web of Science ®Google Scholar
• B. Fuchssteiner and G. Oevel, Geometry and action-angle variables of multisoliton systems, Rev. Math. Phys., 01 (1989) 415. doi: 10.1142/S0129055X8900016X
   Google Scholar
• B. Fuchssteiner, Solitons in Interaction, Prog. Theor. Phys., 65 (1981) 861. doi: 10.1143/PTP.65.861
   Google Scholar
• C. Gardner, J. Greene, M. Kruskal and R. Miura, Method for Solving the Korteweg-de Vries Equation, Physical Review Letters, 19 (1967) 1095–1097. doi: 10.1103/PhysRevLett.19.1095
   Web of Science ®Google Scholar
• R. Hirota, Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971) 1192–1194. doi: 10.1103/PhysRevLett.27.1192
   Web of Science ®Google Scholar
• P.D. Lax, Integrals of Nonlinear Equations of Evolution and Solitary Waves, Communs. Pure. Appl. Math., 21 (1968) 467–490. doi: 10.1002/cpa.3160210503
   Web of Science ®Google Scholar
• W.-X. Ma and Y. You, Solving the Korteweg-de Vries Equation by its Bilinear Form: Wronskian Solutions, Trans. of AMS, 357 (5) (2004) 1753–1778. doi: 10.1090/S0002-9947-04-03726-2
   Web of Science ®Google Scholar
• T.P. Maloney and P.F. Hodnett, A New Perspective on the N-Soliton Solution of the KdV Equation, Proc. of the Royal Irish Academy. Section A: Mathematical and Physical Sciences, 89 (2) (1989) 205– 217.
   Google Scholar
• R. Muira, The Korteweg-de Vries equation. A survey of results, SIAM Review, 18 (1976) 412–59. doi: 10.1137/1018076
   Web of Science ®Google Scholar
• G. Oevel, B. Fuchssteiner, M. Błaszak, Action-angle representation of multisolitons by potential of mastersymmetries, Prog. Theor. Phys., 83 (1990) 395. doi: 10.1143/PTP.83.395
   Google Scholar
• P. Peterson, T. Soomere, J. Engelbrech1, and E. van Groesen, Soliton interaction as a possible model for extreme waves in shallow water, Nonlinear Processes in Geophysics, 10 (2003) 503–510. doi: 10.5194/npg-10-503-2003
   Web of Science ®Google Scholar
• A.G. Rasin, J. Schiff, Unfamiliar Aspects of Backlund Transformations and an Associated Degasperis- Procesi Equation, Theor. Math. Phys., 196 (2018) 1333–1346. doi: 10.1134/S0040577918090076
   Web of Science ®Google Scholar
• G.B. Whitham, Linear and Nonlinear Waves, (Wiley Interscience, New York, 1974).
   Google Scholar
• Y. Yoneyyama, The KdV solution solitons as interacting two single solitons, Prog. Theor. Phys., 71 (1984) 141. doi: 10.1143/PTP.71.843
   Google Scholar
• Z. Yunbo, How to Construct Lax Representation for Constrained Flows of the Boussinesq Hierarchy via Adjoint Representations, Acta Mathematica Scientia, 17 (1997) 97–107. doi: 10.1016/S0252-9602(17)30681-1
   Web of Science ®Google Scholar
• N.J. Zabusky, M.D. Kruskal, Interaction of “Solitons” in a Collisionless Plasma and the Recurrence of Initial States, Phys. Rev. Lett., 15 (1965), 240–243. doi: 10.1103/PhysRevLett.15.240
   Web of Science ®Google Scholar
• J. Zhou, X.-G. Li, D.-S. Wang, The Wronskian Solution and Soliton Resonance of the Nonisospectral Generalised Sawada–Kotera Equation, Z. Naturforschung, 70 (2015) 213–223. doi: 10.1515/zna-2014-0227
   Google Scholar
• B. Xia, R. Zhou, and Z. Qiao, Darboux transformation and multi-soliton solutions of the Camassa-Holm equation and modified Camassa-Holm equation, J. of Math. Phys., 57 (2016). doi: 10.1063/1.4964256
   Web of Science ®Google Scholar