General high-order lump solutions and their dynamics in the Levi equations

Abstract

General high-order lump solutions are derived for the Levi equations based on the Hirota bilinear method and Kadomtsev–Petviashvili (KP) hierarchy reduction technique. These lump solutions are given in terms of Gram determinants whose matrix elements are connected to Schur polynomials. Thus, our solutions have explicit algebraic expressions. Their dynamic behaviors are analyzed by using density maps. It is shown that when the absolute value of one group of these internal parameters in the lump solutions is very large, lump solutions exhibit obvious geometric structures. Interestingly, we have shown that their initial and middle state solutions possess various exciting geometric patterns, including hexagon, decagon, tetradecagon, etc. and other quasi-structures in addition to the standard triangle, pentagon type patterns. Because the internal parameters are not complex conjugates of each other, the dynamic behaviors of solutions are richer. These results make several contributions to the current literature and have a number of important implications for further analysis of fluid dynamics in non-homogeneous media.

Variations of Interatomic Force Constants in the Topological Phonon Phase Transition of AlGaN

“…Both k-mesh sampling grids and kinetic energy cutoffs were examined with careful convergence tests. [7,10,11] Second interatomic FCs (2nd IFCs) were extracted based on the finite displacement supercell approach as implemented in open-source software Phonopy, [13] with a supercell size of 5 Â 5 Â 3 for wurtzite structure and corresponding 3 Â 3 Â 3 k-mesh grids. The Born effective charges and highfrequency dielectric constants were calculated by density functional perturbation theory for nonanalytical corrections of the dynamical matrix near the Gamma point in phonon dispersion calculations brought from polar effects.…”

“…[33] More calculation details can be found in Supporting Information and refs. [8,11,34,35]. To model the alloy structures and their phonon properties, both the VCA method and SQS method [36] were used in this work.…”

“…In the GaN high-electron-mobility transistors (HEMTs), a very important GaN-based electronic, the near-junction thermal management, becomes critical, where heat spreading and phonon ballistic-diffusive thermal transport are coupled and contribute the most to the total thermal resistance. [4,5] In order to tackle the critical heat dissipation issues in GaNbased high-power electronics, first-principles calculations and thermal-physical experiments have been used to reveal the lattice thermal transport rules in single-crystal nitride semiconductors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] as well as their alloy systems. [10,12,22] It has been recently reported that wurtzite III-nitride semiconductors contain topological phonons such as Weyl phonons and nodal ring phonons, [8,11,23,24] which are promising for realizing nondissipative or low-dissipative phonon thermal transport at surfaces and interfaces and improving the near-junction thermal management significantly due to the topologically protected surface phonon states.…”

“…[4,5] In order to tackle the critical heat dissipation issues in GaNbased high-power electronics, first-principles calculations and thermal-physical experiments have been used to reveal the lattice thermal transport rules in single-crystal nitride semiconductors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] as well as their alloy systems. [10,12,22] It has been recently reported that wurtzite III-nitride semiconductors contain topological phonons such as Weyl phonons and nodal ring phonons, [8,11,23,24] which are promising for realizing nondissipative or low-dissipative phonon thermal transport at surfaces and interfaces and improving the near-junction thermal management significantly due to the topologically protected surface phonon states. However, different from the topological phonons protected by the crystalline and time reversal symmetry, these Weyl phonons are the results of accidental degeneracy and not protected by any specific lattice symmetry.…”

“…In the GaN high‐electron‐mobility transistors (HEMTs), a very important GaN‐based electronic, the near‐junction thermal management, becomes critical, where heat spreading and phonon ballistic–diffusive thermal transport are coupled and contribute the most to the total thermal resistance. [ 4,5 ] In order to tackle the critical heat dissipation issues in GaN‐based high‐power electronics, first‐principles calculations and thermal–physical experiments have been used to reveal the lattice thermal transport rules in single‐crystal nitride semiconductors [ 6–21 ] as well as their alloy systems. [ 10,12,22 ]…”