45 citations · 513 across the 36 of their papers we have counts for
5 papers · 1 filter
Soliton interactions and Yang-Baxter maps for the complex coupled short-pulse equation
Vincent Caudrelier, Aikaterini Gkogkou, Barbara Prinari
The complex coupled short pulse equation (ccSPE) describes the propagation of ultra-short optical pulses in nonlinear birefringent fibers. The system admits a variety of vector sol…
Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
Vincent Caudrelier, Nicolas Crampe, Eric Ragoucy +1
We explore the phenomena of absorption/emission of solitons by an integrable boundary for the nonlinear Schrödinger equation on the half-line. This is based on the investigation of…
Lagrangian multiforms on Lie groups and non-commuting flows
Vincent Caudrelier, Frank Nijhoff, Duncan Sleigh +1
We describe a variational framework for non-commuting flows, extending the theories of Lagrangian multiforms and pluri-Lagrangian systems, which have gained prominence in recent ye…
Classical Yang-Baxter equation, Lagrangian multiforms and ultralocal integrable hierarchies
Vincent Caudrelier, Matteo Stoppato, Benoit Vicedo
We cast the classical Yang-Baxter equation (CYBE) in a variational context for the first time, by relating it to the theory of Lagrangian multiforms, a framework designed to captur…
Lagrangian multiforms for Kadomtsev-Petviashvili (KP) and the Gelfand-Dickey hierarchy
Duncan Sleigh, Frank Nijhoff, Vincent Caudrelier
We present, for the first time, a Lagrangian multiform for the complete Kadomtsev-Petviashvili (KP) hierarchy -- a single variational object that generates the whole hierarchy and…