The investigation centers on a generalized Toda lattice equation featuring four potentials.Initially,the continuous counterpart is first established using the continuous limit approach.Subsequently,leveraging its 3...The investigation centers on a generalized Toda lattice equation featuring four potentials.Initially,the continuous counterpart is first established using the continuous limit approach.Subsequently,leveraging its 3×3 matrix spectrum problem,the discrete generalized(m,3N-m)-fold Darboux transformation(DT)is formulated for this discrete system.Finally,the derived generalized DT is employed to generate precise rational solutions and hybrid rational-exponential solutions,which are thoroughly analyzed and graphically illustrated.These novel findings may offer insights into the lattice dynamical phenomena described by Toda lattice equation.展开更多
基金supported by National Natural Science Foundation of China(Grant No.12071042)Beijing Municipal Natural Science Foundation(Grant No.1242004)。
文摘The investigation centers on a generalized Toda lattice equation featuring four potentials.Initially,the continuous counterpart is first established using the continuous limit approach.Subsequently,leveraging its 3×3 matrix spectrum problem,the discrete generalized(m,3N-m)-fold Darboux transformation(DT)is formulated for this discrete system.Finally,the derived generalized DT is employed to generate precise rational solutions and hybrid rational-exponential solutions,which are thoroughly analyzed and graphically illustrated.These novel findings may offer insights into the lattice dynamical phenomena described by Toda lattice equation.
