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An extended Petviashvili method for the numerical generation of traveling and localized waves
Affiliation:1. Department of Applied Mathematics, University of Valladolid, Paseo del Cauce 59, 47011 Valladolid, Spain;2. IMUVA, Institute of Mathematics of University of Valladolid, Spain;3. Department of Applied Mathematics, University of Valladolid, Paseo de Belen 15, 47011 Valladolid, Spain;1. Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu 210023, PR China;2. School of Automation, Southeast University, Nanjing, 210096, PR China;3. Institute of Information and Control Engineering Technology, Nanjing Normal University, Nanjing, Jiangsu 210042, PR China;4. College of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, Jiangsu 210042, PR China;1. Department of Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650500, PR China;2. School of Mathematics and Statistics, Yunnan University, Kunming 650091, PR China;1. College of Science, Shandong University of Science and Technology, Qingdao 266590, PR China;2. Shandong Key Laboratory of Robotics and Intelligent Technology, Qingdao 266590, PR China;1. MOE Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;2. College of Information Engineering, Tarim University, Alar, Xinjiang 843300, China;3. School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China;1. School of Mathematical Sciences and Physics, North China Electric Power University, Beijing 102206, China;2. School of Economics and Management, North China Electric Power University, Beijing 102206, China
Abstract:A family of fixed-point iterations is proposed for the numerical computation of traveling waves and localized ground states. The methods are extended versions of Petviashvili type, and they are applicable when the nonlinear term of the system contains homogeneous functions of different degree. The methods are described and applied to several examples of interest, that calibrate their efficiency.
Keywords:Petviashvili type methods  Solitary wave generation  Iterative methods for nonlinear systems  Ground state generation
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