In this paper, the tanh and sine–cosine methods are used to construct exact periodic and soliton solutions of nonlinear evolution equations arising in mathematical physics. Many new families of exact travelling wave solutions of the generalized Hirota–Satsuma coupled KdV system, generalized-Zakharov equations and (2 + 1)-dimensional Broer–Kaup– Kupershmidt system are successfully obtained. The ...

Using the second flow the Derivative Reaction-Diffusion system, and the third one of the dissipative SL(2,R) Kaup-Newell hierarchy, we show that the product of two functions, satisfying those systems is a solution of the modified Kadomtsev-Petviashvili equation in 2+1 dimension with negative dispersion (MKP-II). We construct Hirota’s bilinear representation for both flows and combine them toget...

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of...

4 KARL-HEINZ GARTEMANN, BIRTE ABT, THOMAS BEKEL, ANNETTE BURGER, 5 JUTTA ENGEMANN, MONIKA FLÜGEL, 1 LARS GAIGALAT, ALEXANDER 6 GOESMANN, INES GRÄFEN, JÖRN KALINOWSKI, OLAF KAUP, OLIVER 7 KIRCHNER, LUTZ KRAUSE, BURKHARD LINKE, ALICE McHARDY, FOLKER 8 MEYER,‡ SANDRA POHLE, CHRISTIAN RÜCKERT, 2,3 SUSANNE SCHNEIKER, EVA9 MARIA ZELLERMANN, ALFRED PÜHLER, RUDOLF EICHENLAUB,* OLAF 10 KAISER, AND DANIE...

Nonlocal reductions of a nonisospectral (2+1)-dimensional breaking soliton Ablowitz-Kaup-Newell-Segur equation are discussed on the base double Wronskian reduction technique. Various types solutions, including solutions and Jordan-block for resulting nonlocal equations derived. Dynamics these obtained analyzed illustrated.

The interaction and propagation of optical pulses in a nonlinear waveguide array is described by the discrete nonlinear Schrödinger equation i∂zψn = −D(ψn+1 + ψn−1 − 2ψn) − γ|ψn|ψn, (1) whereD is a dispersion (or diffraction) coefficient, and γ is a measure of the nonlinearity. By means of the variational approximation, we study the discrete soliton solutions of this equation. We use a trial fu...

Many methods have been developed by scientists to find solutions for nonlinear problems. In this paper, the general structure of modified trial equation method (MTEM) is introduced, and MTEM used some exact (2+1)-dimensional Broer-Kaup-Kupershmidt (BKK), Kolmogorov-Petrovskii-Piskunov (KPP) equations. Firstly, an algebraic system obtained reducing partial differential (NLPDE) ordinary under tra...

Late distributive disambiguation, (3), increases reading measures (first pass, total times, regressions) compared to late collective disambiguation, (4). Early distributive disambiguation, (1), does not significantly increase reading measures compared to early collective disambiguation, (2). Interpretation: Potentially ambiguous predicates are interpreted collectively by the processor ⇒ garden-...