Wang, Yujuan; Song, Yongduan Global conservative and multipeakon conservative solutions for the two-component Camassa-Holm system. (English) Zbl 1295.35148 Bound. Value Probl. 2013, Paper No. 165, 23 p. (2013). Summary: The continuation of solutions for the two-component Camassa-Holm system after wave breaking is studied in this paper. The global conservative solution is derived first, from which a semigroup and a multipeakon conservative solution are established. In developing the solution, a system transformation based on a skillfully defined characteristic and a set of newly introduced variables is used. It is the transformation, together with the associated properties, that allows for the establishment of the results for continuity of the solution beyond collision time. Cited in 1 Document MSC: 35B60 Continuation and prolongation of solutions to PDEs 35C08 Soliton solutions 35C07 Traveling wave solutions Keywords:Lagrangian system; continuation after wave breaking; continuity beyond collision time PDF BibTeX XML Cite \textit{Y. Wang} and \textit{Y. Song}, Bound. Value Probl. 2013, Paper No. 165, 23 p. (2013; Zbl 1295.35148) Full Text: DOI References: [1] doi:10.1016/0167-2789(81)90004-X · Zbl 1194.37114 · doi:10.1016/0167-2789(81)90004-X [2] doi:10.1103/PhysRevLett.71.1661 · Zbl 0972.35521 · doi:10.1103/PhysRevLett.71.1661 [3] doi:10.1098/rspa.2000.0701 · Zbl 0999.35065 · doi:10.1098/rspa.2000.0701 [4] doi:10.1007/s00205-006-0010-z · Zbl 1105.76013 · doi:10.1007/s00205-006-0010-z [5] doi:10.1080/03605300601088674 · Zbl 1136.35080 · doi:10.1080/03605300601088674 [6] doi:10.1142/S0219891607001045 · Zbl 1128.65065 · doi:10.1142/S0219891607001045 [7] doi:10.1142/S0219530507000857 · Zbl 1139.35378 · doi:10.1142/S0219530507000857 [8] doi:10.1007/s00205-008-0128-2 · Zbl 1169.76010 · doi:10.1007/s00205-008-0128-2 [9] doi:10.1007/BF02392586 · Zbl 0923.76025 · doi:10.1007/BF02392586 [10] doi:10.5802/aif.1757 · doi:10.5802/aif.1757 [11] doi:10.1007/s11005-005-0041-7 · Zbl 1105.35102 · doi:10.1007/s11005-005-0041-7 [12] doi:10.1088/0305-4470/39/2/004 · Zbl 1084.37053 · doi:10.1088/0305-4470/39/2/004 [13] doi:10.1016/j.physleta.2008.10.050 · Zbl 1227.76016 · doi:10.1016/j.physleta.2008.10.050 [14] doi:10.1007/s00209-009-0660-2 · Zbl 1228.35092 · doi:10.1007/s00209-009-0660-2 [15] doi:10.1016/j.jde.2009.08.002 · Zbl 1190.35039 · doi:10.1016/j.jde.2009.08.002 [16] doi:10.1016/j.jfa.2010.02.008 · Zbl 1189.35254 · doi:10.1016/j.jfa.2010.02.008 [17] doi:10.1016/j.jfa.2010.11.015 · Zbl 1210.35209 · doi:10.1016/j.jfa.2010.11.015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.