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Free, publiclyaccessible full text available August 1, 2023

Abstract We write down and characterize a large class of nonsingular multisoliton solutions of the defocusing Davey–Stewartson II equation. In particular we study their asymptotics at space infinities as well as their interaction patterns in the xy plane, and we identify several subclasses of solutions. Many of these solutions describe phenomena of soliton resonance and web structure. We identify a subclass of solutions that is the analogue of the soliton solutions of the Kadomtsev–Petviashvili II equation. In addition to this subclass, however, we show that more general solutions exist, describing phenomena that have no counterpart in the Kadomtsev–Petviashvili equation, including Vshape solutions and soliton reconnection.Free, publiclyaccessible full text available July 7, 2023

Abstract We characterize initial value problems for the defocusing Manakov system (coupled twocomponent nonlinear Schrödinger equation) with nonzero background and welldefined spatial parity symmetry (i.e., when each of the components of the solution is either even or odd), corresponding to boundary value problems on the half line with Dirichlet or Neumann boundary conditions at the origin. We identify the symmetries of the eigenfunctions arising from the spatial parity of the solution, and we determine the corresponding symmetries of the scattering data (reflection coefficients, discrete spectrum and norming constants). All parity induced symmetries are found to be more complicated than in the scalar (i.e., onecomponent) case. In particular, we show that the discrete eigenvalues giving rise to dark solitons arise in symmetric quartets, and those giving rise to dark–bright solitons in symmetric octets. We also characterize the differences between the purely even or purely odd case (in which both components are either even or odd functions of x ) and the ‘mixed parity’ cases (in which one component is even while the other is odd). Finally, we show how, in each case, the spatial symmetry yields a constraint on the possible existence of selfsymmetric eigenvalues, corresponding to stationary solitons, and wemore »Free, publiclyaccessible full text available May 30, 2023

Free, publiclyaccessible full text available May 1, 2023

Resonant Yshaped soliton solutions to the Kadomtsev–Petviashvili II (KPII) equation are modelled as shock solutions to an infinite family of modulation conservation laws. The fully twodimensional soliton modulation equations, valid in the zero dispersion limit of the KPII equation, are demonstrated to reduce to a onedimensional system. In this same limit, the rapid transition from the larger Y soliton stem to the two smaller legs limits to a travelling discontinuity. This discontinuity is a multivalued, weak solution satisfying modified Rankine–Hugoniot jump conditions for the onedimensional modulation equations. These results are applied to analytically describe the dynamics of the Mach reflection problem, Vshaped initial conditions that correspond to a soliton incident upon an inward oblique corner. Modulation theory results show excellent agreement with direct KPII numerical simulation.

Abstract The interaction of an oblique line soliton with a onedimensional dynamic mean flow is analyzed using the Kadomtsev–Petviashvili II (KPII) equation. Building upon previous studies that examined the transmission or trapping of a soliton by a slowly varying rarefaction or oscillatory dispersive shock wave (DSW) in one space and one time dimension, this paper allows for the incident soliton to approach the changing mean flow at a nonzero oblique angle. By deriving invariant quantities of the soliton–mean flow modulation equations—a system of three (1 + 1)dimensional quasilinear, hyperbolic equations for the soliton and mean flow parameters—and positing the initial configuration as a Riemann problem in the modulation variables, it is possible to derive quantitative predictions regarding the evolution of the line soliton within the mean flow. It is found that the interaction between an oblique soliton and a changing mean flow leads to several novel features not observed in the (1 + 1)dimensional reduced problem. Many of these interesting dynamics arise from the unique structure of the modulation equations that are nonstrictly hyperbolic, including a welldefined multivalued solution interpreted as a solution of the (2 + 1)dimensional soliton–mean modulation equations, in which the soliton interacts with the mean flowmore »