Riemann-Hilbert problems and N-soliton solutions of the nonlocal reverse space-time Chen-Lee-Liu equation

In this paper,the N-soliton solutions to the nonlocal reverse space-time Chen-Lee-Liu equation have been derived.Under the nonlocal symmetry reduction to the matrix spectral problem,the nonlocal reverse space-time Chen-Lee-Liu equation can be obtained.Based on the spectral problem,the specific matrix Riemann-Hilbert problem is constructed for this nonlocal equation.Through solving this associated Riemann-Hilbert problem,the N-soliton solutions to this nonlocal equation can be obtained in the case of the jump matrix as an identity matrix.

Migration mechanism of atrazine in the simulated lake icing process at different freezing temperatures based on density function theory

Atrazine causes concern due to its resistant to biodegradation and could be accumulated in aquatic organisms,causing pollution in lakes.This study measured the concentration of atrazine in ice and the water under ice through a simulated icing experiment and calculated the distribution coefficient K to characterize its migration ability in the freezing process.Furthermore,density functional theory(DFT)calculations were employed to expatiate the migration law of atrazine during icing process.According to the results,it could release more energy into the environment when atrazine staying in water phase(-15.077 kcal/mol)than staying in ice phase(-14.388 kcal/mol),therefore it was beneficial for the migration of atrazine from ice to water.This explains that during the freezing process,the concentration of atrazine in the ice was lower than that in the water.Thermodynamic calculations indicated thatwhen the temperature decreases from268 to 248 K,the internal energy contribution of the compound of atrazine and ice molecule(water cluster)decreases at the same vibrational frequency,resulting in an increase in the free energy difference of the compound from-167.946 to-165.390 kcal/mol.This demonstrated the diminished migratory capacity of atrazine.This study revealed the environmental behavior of atrazine during lake freezing,which was beneficial for the management of atrazine and other pollutants during freezing and environmental protection.