caa a22 4500 445867973 CHVBK 20180317145503.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1140/epjd/e2010-10357-x doi (NATIONALLICENCE)springer-10.1140/epjd/e2010-10357-x Lax pair, conservation laws and N-soliton solutions for the extended Korteweg-de Vries equations in fluids [Elektronische Daten] [Pan Wang, Bo Tian, Wen-Jun Liu, Qi-Xing Qu, Min Li, Kun Sun] Abstract.: Under investigation in this paper are two extended Korteweg-de Vries (eKdV) equations in fluids with the second-order nonlinear and dispersive terms. Based on the Ablowitz-Kaup-Newell-Segur system, the Lax pair and infinitely many conservation laws are derived. By virtue of the Hirota method and symbolic computation, the bilinear forms and N-soliton solutions for the two eKdV equations are obtained, respectively. Relevant propagation properties and interaction behaviors of the solitons are illustrated graphically. The collisions for the η profile are proved to be elastic through the asymptotic analysis. Types of collisions (head-on or overtaking collisions) can be controlled when we adjust the sign of the velocity v. Velocities of solitons are related to c 4 and α during the collisions. Moreover, there is not a direct proportion relationship between the velocity v and amplitude a during the collisions. On the one hand, the soliton with the larger amplitude travels faster and catches up with the smaller one. On the other hand, the soliton with the smaller amplitude travels faster and catches up with the larger one. EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2011 Wang Pan School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Tian Bo School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Liu Wen-Jun School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Qu Qi-Xing School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Li Min School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Sun Kun School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut The European Physical Journal D Springer-Verlag 61/3(2011-02-01), 701-708 1434-6060 61:3<701 2011 61 10053 https://doi.org/10.1140/epjd/e2010-10357-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1140/epjd/e2010-10357-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Pan School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Tian Bo School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Liu Wen-Jun School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Qu Qi-Xing School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Li Min School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 700 1- Sun Kun School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 773 0- The European Physical Journal D Springer-Verlag 61/3(2011-02-01), 701-708 1434-6060 61:3<701 2011 61 10053 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer