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Homoclinic Orbits and Solitary Waves within the Nondissipative Lorenz Model and KdV Equation

Original article: https://doi.org/10.1142/S0218127420502570

Summary

This open-access IJBC article shows that homoclinic orbits in a three-dimensional nondissipative Lorenz model have the same mathematical form as solitary-wave solutions in the KdV and nonlinear Schrödinger equations. The X and Z components of the Lorenz homoclinic orbit can be written with sech and sech-squared structures, paralleling known solitary-wave forms. The paper uses this correspondence to emphasize mathematical universality across atmospheric models, fluid waves, and nonlinear wave equations, and also relates simplified Lorenz dynamics to error-growth models.

Table comparing the 3D-NLM, Duffing, NLS, KdV, and Logistic equations — Table 1 from Shen (2020), comparing the 3D-NLM, Duffing, nonlinear Schrodinger, Korteweg-de Vries, and Logistic equations. The table summarizes corresponding equation forms and solution types.