34 citations · 36 across the 6 of their papers we have counts for
6 papers
Non-existence of certain elliptic solutions of the Cubic-nonlinear Schrödinger Equation
Hans Werner Schürmann, Valery Serov
For a certain class of solutions of the cubic nonlinear Schödinger equation we prove non-existence in the generic case. In the nongeneric case we present a two-parameter set of sol…
Comment on "Doubly periodic solutions of the focusing nonlinear Schrödinger equation: Recurrence, period doubling, and amplification outside the conventional modulation-instability band"
Hans Werner Schuermann, Valery Serov
In their interesting article (Physical Review A, Vol. 101, 023843 (2020)) Conforti et al. present doubly periodic (elliptic) solutions of the nonlinear Schrödinger equation, based…
Degenerate elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
H. W. Schuermann, V. S. Serov
A subset of traveling wave solutions of the quintic complex Ginzburg-Landau equation (QCGLE) is presented in compact form. The approach consists of the following parts. - Reduction…
Inverse fixed energy scattering problem for the two-dimensional nonlinear Schroedinger operator
Georgios Fotopoulos, Valery Serov
This work studies the direct and inverse fixed energy scattering problem for two-dimensional Schroedinger equation with rather general nonlinear index of refraction. In particular,…
Scattering solutions and Born approximation for the magnetic Schrödinger operator
Valery Serov, Jan Sandhu
We prove the existence of scattering solutions for multidimensional magnetic Schrödinger equation which belong to the weighted Sobolev space H^1_s (R^n)(n=2,3) with some s < -1/2.…
Superposition in nonlinear wave and evolution equations
H. W. Schuermann, V. S. Serov, J. Nickel
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized m…