Soliton solutions for two kinds of fourth-order nonlinear nonlocal Schr?dinger equations

In this paper, we will take two symmetric reduction conditions to obtain two kinds of fourth-order nonlinear nonlocal Schrodinger (NLS) equations, namely the fourth -order nonlocal reverse space and reverse space-time NLS equations. For the former, we will construct one-and N-fold Darboux Transformations (DTs) to obtain the symmetry preserving and broken solutions. In addition, we will study the different combinations of collision scenarios of dark and anti-dark soliton solutions. This process will be expressed in the form of quasi-determinant. Finally, we will get the symmetry preserving and broken solutions can exist at the same time. For the latter, the one-and N-fold DTs will be constructed. Taking the seed solutions as zero and continue wave solutions, we will obtain different kinds of exact solutions under nonlocal constraints, such as soliton, breather and rogue wave solutions, which is different from the classical case.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates two types of fourth-order nonlinear nonlocal Schrodinger (NLS) equations, namely the fourth-order nonlocal reverse space and reverse space-time NLS equations, by using two symmetric reduction conditions. For the former case, one-and N-fold Darboux Transformations (DTs) are constructed to obtain both symmetry preserving and broken solutions, and the collision scenarios of dark and anti-dark soliton solutions are studied. Quasi-determinants are used to express this process. For the latter case, one-and N-fold DTs are constructed, and different types of exact solutions, such as soliton, breather, and rogue wave solutions, are obtained under nonlocal constraints, which differs from the classical case.