In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann the...In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.展开更多
In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized...In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.展开更多
In the current study,we sought to investigate whether T-type Ca^(2+)channels(TCCs)in the brain are involved in generating post-anesthetic hyperexcitatory behaviors(PAHBs).We found that younger rat pups(postnatal days ...In the current study,we sought to investigate whether T-type Ca^(2+)channels(TCCs)in the brain are involved in generating post-anesthetic hyperexcitatory behaviors(PAHBs).We found that younger rat pups(postnatal days 9-11)had a higher incidence of PAHBs and higher PAHB scores than older pups(postnatal days16-18)during emergence from sevoflurane anesthesia.The power spectrum of the theta oscillations(4 Hz-8 Hz)in the prefrontal cortex was significantly enhanced in younger pups when PAHBs occurred,while there were no significant changes in older pups.Both the power of theta oscillations and the level of PAHBs were significantly reduced by the administration of TCC inhibitors.Moreover,the sensitivity of TCCs in the medial dorsal thalamic nucleus to sevoflurane was found to increase with age by investigating the kinetic properties of TCCs in vitro.TCCs were activated by potentiated GABAergic depolarization with a sub-anesthetic dose of sevoflurane(1%).These data suggest that(1)TCCs in the brain contribute to the generation of PAHBs and the concomitant electroencephalographic changes;(2)the stronger inhibitory effect of sevoflurane contributes to the lack of PAHBs in older rats;and(3)the contribution of TCCs to PAHBs is not mediated by a direct effect of sevoflurane on TCCs.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10771196 and 10831003)the Innovation Project of Zhejiang Province of China(Grant No.T200905)
文摘In this paper, a variable-coefficient modified Korteweg-de Vries （vc-mKdV） equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented~ and it is also shown that the soliton solutions can be reduced from the periodic wave solutions.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013QNA41Natural Sciences Foundation of China under Grant Nos.11301527 and 11371361the Construction Project of the Key Discipline in Universities for 12th Five-year Plans by Jiangsu Province
文摘In this paper, a(3+1)-dimensional generalized Kadomtsev–Petviashvili(GKP) equation is investigated,which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. Based on the generalized Bell's polynomials, we succinctly construct the Hirota's bilinear equation to the GKP equation. By virtue of multidimensional Riemann theta functions, a lucid and straightforward way is presented to explicitly construct multiperiodic Riemann theta function periodic waves(quasi-periodic waves) for the(3+1)-dimensional GKP equation. Interestingly,the one-periodic waves are well-known cnoidal waves, which are considered as one-dimensional models of periodic waves.The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional that they have two independent spatial periods in two independent horizontal directions. Finally, we analyze asymptotic behavior of the multiperiodic periodic waves, and rigorously present the relationships between the periodic waves and soliton solutions by a limiting procedure.
基金supported by the National Natural Science Foundation,Beijing,People’s Republic of China(81671058 and 81730031 to YW and 81401089 to MD)the National Research Foundation of Korea grants funded by the Republic of Korea(2019R1I1A1A01057744 to YK)the Foundation of Shanghai Municipal Science and Technology Commission(19ZR1407500 to FS)。
文摘In the current study,we sought to investigate whether T-type Ca^(2+)channels(TCCs)in the brain are involved in generating post-anesthetic hyperexcitatory behaviors(PAHBs).We found that younger rat pups(postnatal days 9-11)had a higher incidence of PAHBs and higher PAHB scores than older pups(postnatal days16-18)during emergence from sevoflurane anesthesia.The power spectrum of the theta oscillations(4 Hz-8 Hz)in the prefrontal cortex was significantly enhanced in younger pups when PAHBs occurred,while there were no significant changes in older pups.Both the power of theta oscillations and the level of PAHBs were significantly reduced by the administration of TCC inhibitors.Moreover,the sensitivity of TCCs in the medial dorsal thalamic nucleus to sevoflurane was found to increase with age by investigating the kinetic properties of TCCs in vitro.TCCs were activated by potentiated GABAergic depolarization with a sub-anesthetic dose of sevoflurane(1%).These data suggest that(1)TCCs in the brain contribute to the generation of PAHBs and the concomitant electroencephalographic changes;(2)the stronger inhibitory effect of sevoflurane contributes to the lack of PAHBs in older rats;and(3)the contribution of TCCs to PAHBs is not mediated by a direct effect of sevoflurane on TCCs.
