In this paper, we prove that the Cauchy problem for Fornberg–Whitham equation is not locally well-posed in Bp,rs(R) with (s,p,r)∈(1,1+1p)×[2,∞)×[1,∞] or (s,p,r)∈{1}×[2,∞)×[1,2] by showing norm inflation phenomena of solution some special initial data.

We consider the use of rational basis functions to compute scattering and inverse transforms associated with AKNS (Ablowitz–Kaup–Newell–Segur) system. The proposed numerical forward transform computes solution system that is valid on entire real axis thereby a reflection coefficient at point by solving single linear makes novel improvement in function approach oscillatory Cauchy operator, enabl...

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...

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Bous...

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...

We prove the existence of highest, cusped, periodic travelling-wave solutions with exact and optimal $ \alpha $-H\"older continuity in a class fractional negative-order dispersive equations form \begin{equation*} u_t + (| \mathrm{D} |^{- \alpha} u n(u) )_x = 0 \end{equation*} for every \in (0, 1) homogeneous Fourier multiplier | |^{ - $. tackle nonlinearities type |^p or |^{p 1} all real p > 1 ...

We present a model of optical communication system for high-bitrate data transmission in the nonreturn-to-zero (NRZ) format over transoceanic distance. The system operates in a small group velocity dispersion regime, and the model equation is given by the Whitham equations describing the slow modulation of multi-phase wavetrains of the (defocusing) nonlinear Schrödinger (NLS) equation. The mode...

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...