½²×ù±àºÅ£ºjz-yjsb-2015-y077
½²×ùÎÊÌ⣺The general traveling wave solutions of the Fisher type equations and some related problems
Ö÷ ½² ÈË£ºÔ¬ÎÄ¿¡ ½ÌÊÚ ¹ãÖÝ´óѧÊýѧÓëÐÅÏ¢ÐÅÏ¢¿ÆѧѧԺ
½²×ùʱ¼ä£º2015Äê11ÔÂ24ÈÕ£¨ÐÇÆÚ¶þ£©ÏÂÖç15:00
½²×ùËùÔÚ£º¸·³É·¶«Ð£ÇøÒ»ºÅÂ¥241ÊÒ
¼ÓÈ빤¾ß£ºÀíѧԺͳ¼ÆרҵµÄÑо¿Éú¼°ÇàÄêÎ÷ϯ
Ö÷Àíµ¥Î»£ºÀíѧԺ
Ö÷½²È˼ò½é£º
Ô¬ÎÄ¿¡£ºÄУ¬ºº×壬ËÄ´¨°²ÔÀÈË¡£1957Äê8ÔÂÉú£¬1998ÄêÀíѧ²©Ê¿£¨»ù´¡Êýѧ¸´ÆÊÎöÆ«Ïò£©½áÒµÓÚÖйú¿ÆѧԺÊýѧÑо¿Ëù£¬Öйú¹²²úµ³µ³Ô±£¬Áôѧ¹é¹úÖ°Ô±£¬¹ãÖÝ´óѧ½ÌÊÚ£¬²©Ê¿Éúµ¼Ê¦¡£ÃÀ¹úÊýѧ̸ÂÛ̸ÂÛÔ±£¬ÖйúÊýѧ»á»áÔ±£¬¹ã¶«Ê¡Öйú¹¤ÒµÓëÓ¦ÓÃÊýѧ»áÀíÊ¡£Êýѧ´Çº£¸´±äº¯ÊýÂÛ±àί£¬¹ú¼ÒÓë¹ã¶«Ê¡×ÔÈ»¿Æѧ»ù½ðÏîÄ¿ÆÀÒéÈË¡£2003-2012ÄêÌìÏ´óѧÉúÊýѧ½¨Ä£¾ºÈü¹ã¶«Ê¡×éί»áίԱ¡£ÔÚÖÖÖÖÆÚ¿¯ÉϽÒÏþѧÊõÑо¿ÂÛÎÄ123ƪ£¬2000ÄêÈνÌÊÚÒÔÀ´È¨Íþ½¹µãÆÚ¿¯»ò¾³ÍâÆÚ¿¯ÉϽÒÏþ69ƪ¡£³öÊéרÖø1²¿£¬½ÒÏþÒëÎÄ5ƪ¡£25´Î±»Ñû¼ÓÈë¹ú¼ÊÐÔѧÊõ¾Û»á£¬ÆäÖÐÔÚÏã¸Û¡¢°ÄÃÅ¡¢ÈÕ±¾¡¢°Ä´óÀûÑǺͺ«¹úµÄ9´Î¾Û»á¶¼»ñµÃÍâ·½µÄ²¿·Ö×ÊÖú¡£±»Ñû²¢»ñ×ÊÖúµ½°Ä´óÀûÑÇ¿ÆÍ¢¿Æ¼¼´óѧ¡¢ÈÕ±¾É½Ðδóѧ¡¢Ïã¸Û¿Æ¼¼´óѧ¡¢Ïã¸Û´óѧ¡¢°ÄÃÅ´óѧ¡¢ÖпÆÔºÊýѧËù¡¢ÄÏ¿ª´óѧ³ÂÊ¡ÉíÊýѧÑо¿ËùµÈº£ÄÚÍâ×ÅÃû´óѧÓëÑо¿Ëù»á¼û20´Î¡£Ö÷³ÖÍê³É¹ú¼Ò×ÔÈ»¿Æѧ»ù½ð¡¢Ê¡²¿¼¶ÏîÄ¿¶àÏî¡£
Ö÷½²ÄÚÈÝ£º
In this talk, we introduce two recent results with respect to the integrality and exact solutions of the Fisher type equations and its applications. We obtain the sufficient and necessary conditions of integral and the general meromorphic solutions of these equations by the complex method. Our results are of the corresponding improvements obtained by many authors. All traveling wave exact solutions of many non-linear partial differential equations are obtained by making use of our results. Our results show that the complex method provides a powerful mathematical tool for solving a large number of nonlinear partial differential equations in mathematical physics. We will propose four analogue problems and expect that the answer is positive, at last.