Nonlinear Dyn https://doi.org/10.1007/s11071-018-4373-0 ORIGINAL PAPER Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations Bo Yang · Yong Chen Received: 15 February 2018 / Accepted: 14 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract A study of high-order solitons in three non- Keywords Nonlocal nonlinear Schrödinger equa- local nonlinear Schrödinger equations is presented. tions · High-order soliton · Riemann–Hilbert method These include the PT -symmetric, reverse-time, and reverse-space-time nonlocal nonlinear Schrödinger equations. General high-order solitons in three different 1 Introduction equations are derived from the same Riemann–Hilbert solutions of the AKNS hierarchy, except for the differ- The integrable nonlinear wave equations and soliton ence in the corresponding symmetry relations on the theory have been studied for many years [1–5]. They “perturbed” scattering data. Dynamics of general high- are signiﬁcant subjects in many branches of nonlin- order solitons in these equations is further analyzed. ear science. For the integrable nonlinear models, most It is shown that the high-order fundamental-soliton is of them are local equations, i.e., the solutions evolu- moving on several different trajectories in nearly equal tion depends only on the local solution value with its local space and time derivatives. Recently, a
Nonlinear Dynamics – Springer Journals
Published: May 29, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera