The stochastic soliton-like solutions of stochastic KdV equations |
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| Affiliation: | 1. Department of Mathematics, Ningbo University, Ningbo 315211, China;2. Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100080, China;3. Department of Physics, Shanghai Jiao-Tong University, Shanghai 200030, China;4. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China;1. Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;1. Fırat University, Science Faculty, Department of Mathematics, 23119, Elazig, Turkey;2. Cankaya University, Department of Mathematics, Ogretmenler Street, 1406530, Ankara, Turkey;3. Institute of Space Sciences, Magurele, Bucharest, Romania;1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt;3. Department of Mathematics, Faculty of Science for Girls, King Abdulaziz University, Jeddah, Saudi Arabia;4. Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USA;5. Department of Mathematics, Kuztown University of Pennsylvania, 15200 Kutztown Road, Kuztown, PA 19530, USA;6. Faculty of Electronic Engineering, Department of Telecommunications, University of Nis, Aleksandra Medvedeva 14, 18000 Nis, Serbia;7. Canino School of Engineering Technology, State University of New York, Canton, NY 13617, USA;8. Department of Mathematics, Howard University, Washington, DC 20059, USA;9. Applied and Industrial Mathematics Research Group, School of Physical, Environmental and Mathematical Sciences, UNSW, Canberra, ACT 2600, Australia;1. Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia;2. Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy;3. Department of Mathematics, Faculty of science, Jazan University, P.O Box 218, Jazan, Saudi Arabia;4. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia;5. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;1. Department of Basic Science, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 08, Kaélé, Cameroon;2. Laboratory of Mechanics, Materials and Structures, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon;3. Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon;4. Department of Marine Engineering, Limbe Nautical Arts and Fisheries Institute, P.O. Box 485, Limbe, Cameroon;5. Department of Mathematics, Lafayette College, Easton, PA, USA;6. Biruni University, Department of Computer Engineering, Istanbul, Turkey;7. Fırat University, Science Faculty, Department of Mathematics, 23119 Elazig, Turkey;8. Department of Medical Research, China Medical University Hospital, China Medical University Taichung, Taiwan,;9. National Advanced School of Engineering, University of Yaounde I, Cameroon |
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| Abstract: | By means of a generalized method and symbolic computation, we consider a stochastic KdV equation Ut + f(t)U ♢ Ux + g(t)Uxxx = W(t) ♢ R♢(t, U, Ux, Uxxx). We construct new and more general formal solutions. At the same time, we recover all the solutions found by Xie [Phys. Lett. A 310 (2003) 161]. The solutions obtained include the nontravelling wave and coefficient function’s stochastic soliton-like solutions, singular stochastic soliton-like solutions, stochastic triangular functions solutions. |
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