Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Based on the Hirota bilinear and long wave limit methods,the hybrid solutions of m-lump with n-soliton and nbreather wave for generalized Hirota–Satsuma–Ito(GHSI)equation are constructed.Then,by approximating solutions of the GHSI equation along some parallel orbits at infinity,the trajectory equation of a lump wave before and after collisions with n-soliton and n-breather wave are studied,and the expressions of phase shift for lump wave before and after collisions are given.Furthermore,it is revealed that collisions between the lump wave and other waves are elastic,the corresponding collision diagrams are used to further explain.

The Bright Single Pulse Emission from PSR B1133+16

We have conducted a comprehensive investigation into the bright single pulse emission from PSR B1133+16using the Giant Metrewave Radio Telescope.High time resolution data(61μs)were obtained at a center frequency of 322 MHz with a bandwidth of 32 MHz over a continuous observation period of 7.45 hr.A total of 1082 bright pulses were sporadically detected with peak flux densities ranging from 10 to 23 times stronger than the average pulse profile.However,no giant pulse-like emission with a relative pulse energy larger than 10 and extremely short duration was detected,indicating that these bright pulses cannot be categorized as giant pulse emission.The majority of these bright pulses are concentrated in pulse phases at both the leading and trailing windows of the average pulse profile,with an occurrence ratio of approximately 2.74.The pulse energy distribution for all individual pulses can be described by a combination of two Gaussian components and a cutoff power-law with an index of α=-3.2.An updated nulling fraction of 15.35%±0.45% was determined from the energy distribution.The emission of individual pulses follows a log-normal distribution in peak flux density ratio.It is imperative that regular phase drifting in bright pulse sequence is identified in both the leading and trailing components for the first time.Possible physical mechanisms are discussed in detail to provide insights into these observations.