Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides non auto-Bäcklund transformation between two n-th KdV equations with self-consistent sources with different degrees. The formula for the m-times repeated binar...

Huge amount of Arabic information and documents are widely spread on the Internet. The accuracy of searching for Arabic documents, as well as other documents, depends on the terms used by the user in the input query to retrieve relevant results and to reduce irrelevant ones. Most results returned are relevant to the query terms not to its meaning. For example, searching for “ ت ص ل ب ا ل ش ر ا ...

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, bt = bx. Two new discretizations are also given, the ...

The initial value problems for the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations under periodic and decaying boundary conditions are considered. These initial value problems are shown to be globally well-posed in all L 2-based Sobolev spaces H s where local well-posedness is presently known, apart from the H 1 4 (R) endpoint for mKdV. The result for KdV relies on a new method for co...

In this paper, we derive a Bäcklund transformation for the supersymmetric Kortwegde Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Kortweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 1984....

In this paper, we derive a Bäcklund transformation for the supersymmetric Korteweg-de Vries equation. We also construct a nonlinear superposition formula, which allows us to rebuild systematically for the supersymmetric KdV equation the soliton solutions of Carstea, Ramani and Grammaticos. The celebrated Korteweg-de Vries (KdV) equation was extended into super framework by Kupershmidt [3] in 19...

کچ ی هد هکبش هکبش رگسح یاه رگسح زا یا هنیزه مک و دودمح یژرنا اب ،کچوک یاه دنتسه یا یم شخپ رظن دروم هقطنم رد هک هداد ات دنوش عجم طیمح زا ار ییاه شزادرپ یارب و هدونم یروآ یزکرم هرگ هب ١ دننک لاسرا . م نینچهم ی هب و هداد صیخشت طیمح رد ار یدادخر عوقو دنناوت دنناسرب یزکرم هرگ علاطا . هکبش هنوگنیا ریخا یالهاس رد هنیمز رد اه یاهدربراک فلتمخ یاه هدرک ادیپ یدایز دنا . زا دنترابع اهدربراک نیا هلجم زا...

In this paper we present an overview of the direct relation between differential invariants of projective type for curves in flat semisimple homegenous spaces and PDEs of KdV type. We describe the progress in the proof of a conjectured Theorem stating that for any such space there are geometric evolutions of curves that induce completely integrable evolutions on their invariants of projective-t...